. 


MECHANICAL 
DRAWING  PROBLEMS 


BOOKS  BY 
CHARLES  WILLIAM  WEICK,  B.  Sc. 

ELEMENTARY  MECHANICAL  DRAWING. 
250  pages,  6x9,  324  Illustrations $1.75 

MECHANICAL  DRAWING  PROBLEMS. 
153  pages,   6x9,  48  Illustrations   and 

112  Plates $1.25 

IN  PREPARATION 

MACHINE  DRAWING  PROBLEMS 


MECHANICAL 
DRAWING  PROBLEMS 


BY 
CHARLES  WILLIAM  WEICK,  B.  Sc. 

ASSISTANT  PROFESSOR  OF  DRAWING  AND  DESIGN,  TEACHERS  COLLEGE 

COLUMBIA  UNIVERSITY,  IN  THE  CITY  OP  NEW  YORK;  AUTHOR 

OF  "ELEMENTARY  MECHANICAL  DRAWING." 


FIRST  EDITION 


McGRAW-HILL  BOOK  COMPANY,  INC. 
239  WEST  39TH  STREET,    NEW  YORK 


LONDON:  HILL  PUBLISHING  CO.,  LTD. 

6  &  8  BOUVERIE  ST.,  E.  C. 

1917 


COPYRIGHT,  1917,  BY  THE 
MCGEAW-HILL  BOOK  COMPANY,  INC. 


PREFACE 

This  volume  is  a  book  of  examples  and  problems  for  the  study  of 
mechanical  drawing.  It  is  intended  to  be  used  under  the  direc- 
tion of  a  teacher,  although  the  ambitious  and  painstaking  student 
can  solve  many  of  the  problems  without  such  aid.  It  aims  to 
provide  a  large  selection  of  typical  drawings  carefully  worked  out 
as  examples,  each  one  of  which  is  accompanied  by  appropriate 
problems  suitable  for  elementary  and  advanced  work  in  mechan- 
ical drawing.  Explanations  and  directions  are,  when  needed, 
expressed  in  simple  and  direct  language,  and  in  the  fewest  possible 
words.  The  principles  of  the  construction  of  a  drawing  are 
shown  in  the  examples  in  the  graphic  language  of  the  draftsman. 

The  book  is  divided  into  three  parts.  The  First  Part  gives 
in  brief  outline  such  matter  as  the  student  will  need  to  know 
before  beginning  work.  It  contains,  also,  a  limited  number  of 
geometrical  constructions  which  will  be  found  helpful  in  solving 
some  of  the  problems  given. 

The  Second  Part — the  practical  work — is  divided  into  four 
sections,  namely:  Projections,  Developments  and  Intersections, 
Isometric  Drawings,  and  Machine  Details.  Nearly  all  the 
example-drawings  are  fully  dimensioned  and,  where  necessary, 
described  by  explanatory  notes.  They  are  not  to  be  copied  but 
are  intended  to  serve  as  a  guide  to  the  student  when  making  his 
own  drawings  for  which  directions  are  given  in  the  form  of 
problems.  In  each  section  there  are  many  more  problems  than 
any  one  student  can  work  in  the  amount  of  time  which  is  usually 
allotted  to  the  subject  of  mechanical  drawing,  and  a  judicious 
selection  must  necessarily  be  made  by  the  teacher  to  meet  the 
individual  student's  requirement.  These  problems  are  arranged 
in  the  order  of  their  difficulty.  The  problems  given  in  the  begin- 
ning of  each  section  are  not  too  difficult  for  a  beginner  in  mechan- 
ical drawing,  while  those  toward  the  end  of  the  sections  will  be 
found  suitable  for  advanced  students.  Each  section  begins  with 
problems  that  are  suitable  for  Junior  High  Schools,  High  Schools, 
and  Evening  Schools,  and  advances  gradually  to  problems  that 
are  more  difficult  of  solution,  suitable  for  Vocational  Schools, 
Trade  Schools,  and  Colleges.  In  the  first  three  sections  two 


vi  PREFACE 

problems  are  given  with  each  example-drawing,  and  in  the  fourth 
section,  three  problems  are  given. 

The  problems  on  Developments  and  Intersections  are  suitable 
as  an  introductory  course  for  students  interested  in  sheet  metal 
pattern  drafting.  The  problems  on  Machine  Details  will  form  a 
logical  introduction  to  machine  design. 

The  Third  Part  of  the  book  contains  tables  and  general  infor- 
mation of  use  to  draftsmen,  and  to  which  frequent  reference 
should  be  made  when  working  problems  in  the  second  and  fourth 
sections  of  the  Second  Part. 

The  author's  not  inconsiderable  experience  as  draftsman  and 
designer  of  machinery,  and  as  teacher  of  drawing  and  design, 
leads  him  to  believe  that  teachers  will  find  sufficient  material  in 
the  following  pages  to  enable  them  to  formulate  suitable  courses 
for  classes  in  mechanical  drawing  for  all  schools  where  this  subject 
is  taught. 

The  author  is  indebted  to  many  books  on  mechanical  drawing 
for  helpful  suggestions  in  the  preparation  of  the  drawings  of  this 
volume,  especially  to  Professor  Thomas  E.  French's  "Engineering 
Drawing."     In    preparing    the    manuscript    and    drawings    he 
gratefully  acknowledges  much  valuable  help  he  has  received  from 
Mr.  Arthur  F.  Hopper,  director  of  manual  arts,  Plainfield,  New 
Jersey;  Mr.  Frank  C.  Panuska,  instructor  in  mechanical  drawing, 
and  Mr.  Ralph  Breiling,  of  Teachers  College. 
NEW  YORK, 
October,  1917 


CONTENTS 

PREFACE    

PART  I.— INTRODUCTION 
GENERAL  INFORMATION. 


Instruments  and  Materials 

PAGE 
1 

Drawing  Lrnes  . 

1 

Lines  Used  
Border  Lines  
Lettering  
Dimensions  

-.   .      2 
2 
.............      4 
.       6 

Titles  
Sharpening  Pencils 

7 
9 

Penciling  
Sequence  for  Penciling  
Inking  
Sequence  for  Inking  
Use  of  Lines  
Location  of  Views  
Working  Drawings  

10 
10 
10 
10 

11 
11 

.    .    12 

GEOMETRIC  CONSTRUCTIONS. 

To  Bisect  a  Given  Angle 13 

To  Bisect  a  Given  Arc 13 

To  Set  Off  an  Angle  Equal  to  a  Given  Angle  from  a  Point  on  a 

Given  Line ,  .     13 

To  Divide  a  Given  Line  into  Any  Number  of  Equal  Parts ....      14 
To  Find  the  Point  of  Tangency  of  a  Given  Circular  Arc  and  a 

Given  Straight  Line 14 

To  Find  the  Point  of  Tangency  of  Two  Given  Circular  Arcs.     .    .      14 
To  Draw  an  Arc  of  Given  Radius  Tangent  to  Two  Straight  Lines 

Meeting  at  Right  Angles 15 

To  Draw  an  Arc  of  Given  Radius  Tangent  to  Two  Intersecting 

Straight  Lines 15 

To  Draw  an  Arc  of  Given  Radius  Tangent  to  a  Given  Straight  Line 

and  a  Given  Circular  Arc 15 

To  Draw  a  Circular  Arc  Tangent  to  a  Given  Straight  Line  and 

Tangent  at  a  Point  on  a  Given  Circular  Arc 16 

To  Connect  Two  Given  Parallel  Lines  with  a  Compound  Curve  aad 

Tangent  at  Given  Points 16 

To  Draw  a  Circular  Arc  of  Given  Radius  Tangent  to  Two  Given 

Circular  Arcs 16 

To  Construct  a  Regular  Polygon  of  Any  Number  of  Sides  Within  a 

Circle  of  Given  Diameter.    .  17 


viii  CONTENTS 

PAGE 

To  Construct  a  Regular  Polygon  of  Any  Number  of  Sides  on  a 

Line  of  Given  Length 18 

To  Draw  an  Ellipse,  the  Major  and  Minor  Axes  Being  Given    ...     18 
To  Draw  an  Approximate  Ellipse,  the  Major  and  Minor  Axes  Being 
Given 18 

CONVENTIONAL  SCREW  THREADS 

Screw  Threads 19 

INTERSECTION  OF  Two  CYLINDERS. 

To  Find  the  Line  of  Intersection  of  Two  Cylinders  with  Axes  in 
the  Same  Plane  and  at  Right  Angles  to  Each  Other 20 

PLANE  INTERSECTION  OF  A  SOLID. 

To  Find  the  Lines  of  Intersection  of  a  Surface  of  Revolution  Cut  by 
Two  Planes  at  Right  Angles  to  Each  Other  and  Parallel  to  the  Axis.     21 

PART  II.— EXAMPLES  AND  PROBLEMS 

PROJECTIONS. 

Section  I.— Thirty  Examples— Sixty  Problems 23-53 

DEVELOPMENTS  AND  INTERSECTIONS. 

Section  II. — Thirty-six  Examples — Seventy-two  Problems.    .     .   54-95 

ISOMETRIC  DRAWING. 

Section  III. — Twenty-two  Examples — Forty-four  Problems.       96-117 

MACHINE  DETAILS. 

Section  IV.— Twenty-four  Examples— Seventy  Problems  .    .    118-141 

PART  III.— TABLES 

LTRT  OF  TABLES. 

I.  Cap  Screws • 144 

II.  U.S.  Standard  Bolts   and  Nuts 145 

III.  Machine  Screws 146 

IV.  Briggs  Standard  Pipe  Threads 147 

V.  Set  Screws 148 

VI.  Gib  Keys ;    ,  ' 148 

VII.  Feather  Keys  or  Splines 148 

VIII.  Automobile  Screws  and  Nuts 149 

IX.  Jarno  Tapers 150 

X.  Morse  Tapers !..... 150 

XI.  Decimal  Equivalents 151 

XII.  Areas  and  Circumferences  of  Circles 152 

Conventional  Section  Lines  .                                           153 


LIST  OF  PLATES 

SECTION  I 
PROJECTIONS 

PAGE 

1.  Prism 25 

2.  Tapered  Objects 25 

3.  Circular  Objects 27 

4.  Geometric  Objects 27 

5.  Geometric  Object 29 

6.  Geometric  Solid 29 

7.  Projection  of  Letter 31 

8.  Projection  of  Letter 31 

9.  Hollow  Cylinder 33 

10.  Geometric  Solid 33 

11.  Projection  of  Letter 35 

12.  Projection  of  Letter 35 

13.  Triangular  Prism .    .    .    , 37 

14.  Pentagonal  Prism 37 

15.  Square  Pyramid 39 

16.  Hexagonal  Pyramid 39 

17.  Right  Cone 41 

18.  Right  Cylinder '41 

19.  Square  Prisms 43 

20.  Cross  and  Prism 43 

21.  Letter  and  Prism ' 45 

22.  Letter  and  Prism 45 

23.  Cylinder  and  Prism 47 

24.  Cone  and  Cylinder 47 

25.  Projection  Problems 49 

26.  Projection  Problems 49 

27.  Projection  Problems 51 

28.  Projection  Problems 51 

29.  Projection  Problems 53 

30.  Projection  Problems 53 

SECTION  II 
DEVELOPMENTS  AND  INTERSECTIONS 

31.  Rectangular  Prism 55 

32.  Truncated  Rectangular  Prism 55 

33.  Triangular  Wedge 57 

34.  Truncated  Square  Prism 57 

ix 


x  LIST  OF  PLATES 

PAGE 

35.  Truncated  Triangular  Prism 59 

36.  Truncated  Hexagonal  Prism 59 

37.  Truncated  Pentagonal  Prism 61 

38.  Triangular  Pyramid 61 

39.  Truncated  Square  Pyramid 63 

40.  Scalene  Pyramid 63 

41.  Truncated  Cylinder 65 

42.  Truncated  Cone 65 

43.  Conic  Section 67 

44.  Conic  Section 67 

45.  Intersecting  Cylinders 69 

46.  Intersecting  Solids 69 

47.  Cone  and  Cylinder 71 

48.  Cone  and  Prism 71 

49.  Three-Piece  Elbow 73 

50.  Vertical  and  Oblique  Cylinders 73 

51.  Circular  Offset  Pipe 75 

52.  Three-Piece  Conical  Elbow 75 

53.  Intersecting  Pipes 77 

54.  Intersecting  Pipes 77 

55.  Transition  Piece 79 

56.  Transition  Piece 79 

57.  Scalene  Cone 81 

58.  Transition  Piece 81 

59.  Intersection  of  Two  Prisms 83 

60.  Development  of  Two  Intersecting  Prisms 83 

61.  Intersection  of  Two  Cones 85 

62.  Development  of  Two  Intersecting  Cones 85 

63.  Intersection  of  Two  Cones 87 

64.  Development  of  Two  Intersecting  Cones 87 

65.  Intersection  of  Two  Cones 89 

66.  Development  of  Two  Intersecting  Cones 89 

Supplementary  Problems 90-96 

SECTION  III 
ISOMETRIC  DRAWING 

67.  Isometric  Blocks 97 

68.  Joints 97 

69.  Joints 99 

70.  Mortise  and  Tenon  Joints 99 

71.  Miter  Box 101 

72.  Drawer  and  Table  Joints 101 

73.  Box  with  Hinged  Lid 103 

74.  Sawhorse ' 103 

75.  Isometric  Prisms 105 

76.  Prisms  .  .    105 


LIST  OF  PLATES  xi 

PAGE 

77.  Isometric  Circles 107 

78.  Isometric  Arcs 107 

79.  Hollow  Cylinder 109 

80.  Bearing  Cap 109 

81.  Magnet  Pole  Pieces Ill 

82.  Milling  Cutter  and  Face  Plate Ill 

83.  Knife  and  Fork  Box 113 

84.  Uniform  Motion  Cam 113 

85.  Bracket  Shelf 115 

86.  Kitchen  Table 115 

87.  Knuckle  Joint 117 

88.  Small  Bench 117 

SECTION  IV 
MACHINE  DETAILS 

89.  Eccentric  Sheave 119 

90.  Hand-Wheel 119 

91.  Engine  Crank 121 

92.  Connecting-Rod  End 121 

93.  Crane  Hook 123 

94.  Clutch  Couplings 123^ 

95.  Screw  Threads 125" 

96.  Bolts  and  Nuts 125 

97.  Lathe  Carrier 127 

98.  Clamp  Coupling 127 

99.  Stuffing  Box 129 

100.  Safety  Coupling      129 

101.  Nut  Coupling      131 

102.  Forked  Rod 131 

103.  Shifting  Gear 133 

104.  Planer  Jack 133 

105.  Belt  Pulley 135 

106.  Belt  Pulley 135 

107.  Grease  Cup      137 

108.  Lathe  Chuck   ....    .~ 137 

109.  Pipe  Union 139 

110.  Pipe  Union 139 

111.  Screw  Jack 141 

112.  Ball  Bearing 141 


MECHANICAL 
DRAWING  PROBLEMS 

PART  I 
INTRODUCTION 

GENERAL  INFORMATION 

Instruments  and  Materials. — To  obtain  good  results  in 
mechanical  drawing  a  good  set  of  drawing  instruments  is  neces- 
sary. Economy  in  their  purchase  is  unwise,  because  drawings 
made  with  inferior  equipment  will  be  of  inferior  quality  in  tech- 
nique. A  good  set  of  drawing  instruments  with  proper  care  will 
serve  a  draftsman's  needs  almost  a  lifetime.  The  following  list 
of  instruments  and  materials  comprises  a  minimum  equipment 
consistent  with  good  work: 

A  compass  with  pencil  leg,  pen  leg,  and  extension  bar.  Divid- 
ers. Bow  pencil.  Bow  pen.  Two  ruling  pens.  45°  celluloid  tri- 
angle. 30°  X  60°  celluloid  triangle.  Two  celluloid  curves.  Pro- 
tractor. 12-inch  architect's  scale.  Drawing  board.  T-square. 
Pencils.  Sandpaper  pencil  pointer.  Pencil  and  ink  eraser.  Two 
penholders  and  pens  for  lettering.  Penwiper.  Thumb  tacks. 
Cleaning  rubber.  Drawing  paper  and  drawing  ink. 

Drawing  Lines. — Draw  horizontal  lines  at  the  upper  edge  of  the 
T-square  blade;  never  draw  lines  at  its  lower  edge.  Draw  verti- 
cal lines,  and  lines  making  angles  15°,  30°,  45°,  60°,  and  75°  with 
the  triangles  resting  against  the  T-square  blade.  Lines  making 
angles  other  than  those  mentioned  are  drawn  by  the  aid  of  the 
T-square,  or  the  triangle,  placed  in  the  desired  position. 

Fig.  1  shows  the  method  for  drawing  lines  perpendicular  to,  and 
also  lines  making  angles  of  60°,  30°,  and  45°  with  the  T-square 
blade.  The  arrows  shown  on  the  lines  indicate  the  direction  in 
which  the  lines  should  be  drawn.  Fig.  2  shows  methods  for 
drawing  lines  making  angles  of  15°  and  75°  with  the  T-square 
blade. 

1 


2  MECHANICAL  DRAWING  PROBLEMS 

Circles  and  circular  arcs  are  drawn  with  the  compass,  or  the 
bow  instruments.  Irregular  curves  are  drawn  by  aid  of  the  cel- 
luloid curves,  with  pencil  or  ruling  pen. 


90-  6CJ\        760' 


FIG.  1. — Showing  vertical  and  oblique  lines. 


FIG.  2. — Position  of  triangles  for  drawing  15°  and  75°  lines. 


Lines  Used. — The  various  lines  shown  in  Fig.  3  are  of  the  kind 
used  by  most  draftsmen,  and  may  be  considered  as  standard.  In 
drawings  which  are  to  be  inked  or  traced,  continuous  pencil  lines 
may  be  used  where  there  is  no  likelihood  of  an  error  when  inking. 

Border  Lines. — The  object  of  a  border  line  is  to  give  the  draw- 
ing a  finished  appearance.  The  border  line  and  the  trimming  line 
should  be  drawn  in  pencil  before  the  drawing  itself  is  begun,  and 
should  have  the  dimensions  shown  in  Fig.  4.  When  inking,  the 
border  line  should  be  the  last  line  drawn. 


INTRODUCTION 


VISIBLE    OUTLINE 


HIDDEN    OUTLINE 
CENTER     LINE 


PPOUECTION   LINE 


AUXILIARY  LINE 
EXTENSION   LINE 


DIMENSION  LINE 


BORDER    LINE 

FIG.  3. — Conventional  lines. 


- 

£ 
1 

4 

"S 

* 

3 

:    « 

N 

/2 

'2 

/5 

4 

Q 

L 

— 

10 

5  \  

\\\fioflO£R  LINE 
DRAWING  BOARD                   ^CUTTING  LINE: 
X£OGC  or  PAPCR 

FIG.  4. — Layout  of  border  and  cutting  lines. 


4  MECHANICAL  DRAWING  PROBLEMS 

Lettering. — Since  the  general  effect  in  the  appearance  of  a 
drawing  depends  in  a  large  measure  on  the  appearance  of  its  title, 
notes  and  dimensions,  lettering  and  figuring  form  an  essential 
part  of  the  draftsman's  work. 

The  prime  requisite  for  good  lettering  and  figuring  is  simplic- 
ity of  style  and  uniformity  of  treatment.  These  are  obtained  by 
correctness  of  form  of  letters  and  figures,  a  uniform  inclination 
and  height,  and  proper  spacing.  These  results  must  be  obtained 
by  accuracy  of  hand  and  eye,  since  no  rules  can  be  followed  which 
will  be  practical  for  all  combinations  of  letters  and  worde. 

Since  it  is  generally  difficult  for  a  beginner  to  letter  well,  it  will 
be  necessary,  in  order  to  acquire  proficiency  and  obtain  good 
results,  to  devote  some  time  to  the  practice  of  making  letters 
singly  and  in  combinations  to  form  words. 

When  placing  a  title,  notes  or  figures  on  a  drawing  the  begin- 
ner should  always  remember,  no  matter  how  good  a  drawing  may 
be,  or  how  much  time  was  given  to  its  execution,  if  the  lettering  or 
figuring  is  hurriedly  or  carelessly  done,  the  completed  drawing 
will  not  present  a  neat  appearance. 

The  "Gothic,"  or  uniform  line  letters,  shown  in  Fig.  5,  find 
favor  with  draftsmen  and  are  generally  used  for  mechanical 
drawings. 

Limiting  lines  should  always  be  drawn  to  serve  as  a  guide  for 
the  height  and  proper  alignment  of  letters.  They  are  used  by 
the  most  experienced  of  letterers.  Since  it  is  important  that  all 
letters  have  the  same  slant,  slanting  lines  should  be  drawn  to  serve 
as  a  guide  to  the  eye.  These  lines  may  be  drawn  about  one-quar- 
ter inch  apart.  See  Fig.  6.  All  limiting  and  guide  lines  should 
be  drawn  with  a  wedge-pointed  pencil,  and  very  fine  so  they  may 
be  easily  erased.  Letters  and  figures  are  made  with  a  conical- 
pointed  pencil. 

Small  letters  need  not  necessarily  be  drawn  with  the  pencil,  but 
may  be  put  in  directly  with  ink.  Titles  and  large  letters  should 
always  be  drawn  in  pencil  before  inking. 

For  titles  and  large  letters  a  "Hunt's  Extra  Fine  Shot  Point 
Pen,"  Number  512,  and  for  small  letters  and  figures  a  "Hunt's 
Strand  Pen,"  Number  54,  will  be  found  suitable.  "Leonard's 
Ball  Point  Pen,"  Number  506F,  for  large  letters,  and  "Gillott's 
Pen,"  Number  303,  for  small  letters  and  figures,  also  find  favor 
among  many  draftsmen. 

For  practical  work,  the  height  of  letters  and  figures  should  be 


INTRODUCTION 


-LETTERS  AND  FIGURES- 

ABCDEFGHIJKLMN 
OPQRSTUVWXYZ 

12345676  9  O 
EXTENDED      COMPRESSED 


ABCDEFGHIJKLMN 
OPQRSTUVWX     Y   Z 

7234,567690 
ETXTET/VOETO  COMPRESSED 


obcdefgh    i  j   k   I  m    n 
O    p    q    r    s     t    u    v    w    x    y    z 
Lower   Case    Letters 


=4-4 


CAPITALS  FOR  TITLES***® 

CAPITALS      FOR      SUB -TITLES" ^«> 
For   Descriptive    Matter"      *ig 

For   Dimensions    ef    24^. —    M% 


FIG.  5. — Inclined  single-stroke  letters. 


6 


MECHANICAL  DRAWING  PROBLEMS 


as  shown  in  Fig.  5.  The  slant  may  be  from  60°  to  75°,  according 
to  the  judgment  of  the  student;  or,  they  may  be  vertical,  if 
preferable,  as  shown  in  the  last  two  lines  of  Fig.  6. 


FIG.  6. — Showing  use  of  guide  lines. 

Dimensions. — To  dimension  a  drawing  means  to  place  upon  it 
all  measurements  required  for  the  construction  of  the  object 
represented.  Fig.  7  shows  an  object  with  all  dimensions  neces- 
sary for  its  construction. 

Dimensions  are  placed  in  dimension  lines  which  terminate  with 
arrow  heads.  A  break,  or  space,  should  be  left  near  but  not 
necessarily  in  the  center  of  the  lines  to  receive  the  dimensions. 
See  Fig.  7.  Dimensions  should  not  be  placed  on  center  lines. 

There  are  several  ways  for  writing  dimensions;  for  instance, 
four  inches  may  be  written  as  4  inches,  4  in.,  4",  or  simply  4,  the 
accent  sign  (")  being  omitted  when  all  dimensions  of  the  object 
are  in  inches.  The  proper  use  of  the  sign  (")  is  shown  in  Fig.  7. 
Feet  and  inches  are  written  thus;  4  ft.  6  in.,  or,  more  commonly, 
4'-6";  3'-4|";  5'-0",  etc.  The  use  or  omission  of  the  inch  sign, 
which  is  omitted  in  the  following  drawings,  is  left  to  the  judgment 
of  the  instructor. 


INTRODUCTION  7 

Figures  for  whole  numbers  should  be  -&  high,  and  fractions 
should  be  ^  high,  over  all.  The  division  line  of  a  fraction 
should  be  in  line  with  the  dimension  line.  The  figures  of  a  frac- 
tion should  not  touch  the  division  line.  This  requires  that  each 
figure  of  the  fraction  be  a  trifle  less  in  height  than  the  whole  num- 
ber. See  last  line  of  Fig.  5. 


"TT 


r 

wi* 

1 


FIG.  7. — Showing  a  method  for  dimensioning. 


Titles. — The  title  of  a  drawing  may  be  placed  at  the  top  of  the 
sheet  centrally  with  respect  to  the  vertical  lines  of  the  border,  and 
the  problem  number  in  the  upper  left-hand  corner,  as  shown  in 
Fig.  8.  The  distance  marked  x  should  not  exceed  three-quarters 
of  an  inch  in  any  drawing.  In  some  drawings,  depending  on  the 
problem  and  the  arrangement  of  views,  this  distance  will  neces- 
sarily be  somewhat  less,  but  in  no  case  should  it  be  less  than  one- 
half  inch. 

In  working  drawings,  titles  are  always  placed  in  the  lower  right- 
hand  corner,  as  shown  in  Fig.  9,  the  problem  number  in  the  upper 
left-hand  corner  being  omitted.  Fig.  10  shows  three  forms  of 
general  titles.  Any  one  of  these  forms  may  be  adopted  instead  of 
the  titles  shown  in  the  example  drawings. 

It  is  customary  in  some  schools  to  place  titles  of  practice  draw- 
ings at  the  top  of  the  sheet,  and  titles  of  working  drawings  in  the 


8  MECHANICAL  DRAWING  PROBLEMS 

lower  right-hand  corner.  A  slight  readjustment  of  views  in  the 
following  drawings,  which  have  their  titles  on  top,  will  provide 
space  for  titles  in  the  lower  right-hand  corner,  if  preferable. 


FIG.  8. — Title-form  when  placed  on  top. 


TITLE 

DRAWINGS 


BORDER    LINE 
FIG.  9. — Title-form  when  placed  at  bottom. 


^.RECTANGULAR     PRISMS^ 

I    DRAWN    BY  J.H.SMITH         6-12-17^ 


.THREE-PIECE 

-J*  ___  HIHTJZI  SCALE     6  -  /'  =ZZ__iIZI 

~ 


H.  SMITH  UUNE  12   1917 


DESIGN     FOR 


ENGINE  ECCENTRIC? 

^JLH-L  SIZE  6-12-17  ZTZL 

^zf^^ DRAWN    BY    J.  H. SMITH zzi — f— n? 


FIG.  10. — Various  title-forms. 


Before  placing  a  title  on  a  drawing,  it  would  be  well  to  make  a 
trial  title  on  a  separate  piece  of  paper,  as  several  attempts  may  be 
necessary  to  produce  a  satisfactory  result.  When  the  trial  title  is 
found  satisfactory,  it  can  then  be  copied  on  the  drawing. 


INTRODUCTION 


9 


Underscore  lines  drawn  to  a  title,  when  placed  at  the  top  of  the 
drawing,  as  shown  in  Fig.  8,  are  optional  with  the  instructor. 
Their  use,  however,  adds  character  and  stability  to  lettering. 


FIG.  11. — Wedge-shaped  pencil  point. 


FIG.  12. — Cone-shaped  pencil  point. 


FIG.  13. — Correct  position 
of  pencil. 


FIG.  14. — Incorrect  position 
of  pencil. 


Sharpening  Pencils. — For  wedge-shaped  points,  remove  the 
wood  as  shown  in  Fig.  11,  with  a  sharp  knife,  or  a  chisel,  exposing 
the  lead  which  is  then  sharpened  with  a  sandpaper  pencil  pointer 
or  a  fine  file.  Fig.  12  shows  a  cone-pointed  pencil. 


10  MECHANICAL  DRAWING  PROBLEMS 

Fig.  13  shows  the  correct  position  of  the  pencil,  relative  to  the 
T-square  or  triangle,  for  drawing  straight  and  accurate  lines. 
Fig.  14  shows  an  incorrect  position  of  the  pencil. 

Penciling. — For  good  penciling,  which  is  a  prerequisite  to  good 
inking,  two  pencils  should  be  used;  one  5H  for  drawing  lay-out 
lines,  which  are  to  be  drawn  fine,  and  one  4H  for  drawing  lines 
whose  positions  and  limitations  have  been  determined.  These 
pencils  should  be  sharpened  to  long  slender  wedge-shaped  points. 
For  pointing  off  distances,  making  letters,  figures,  and  arrow 
heads,  a  3H  pencil  sharpened  to  a  cone-point  should  be  used. 
Pencils  should  be  sharpened  frequently  to  keep  the  points  in  good 
working  condition.  All  lines  should  be  drawn  as  fine  as  is  con- 
sistent with  clearness. 

Sequence  for  Penciling. — A  general  sequence  for  penciling, 
when  conditions  permit,  may  be  as  follows: 


1.  Draw  border  and  cutting  lines. 

2.  Lay  off  space  required  for  title. 

3.  Decide  on  number  of  views  required. 

4.  Make  a  rough,  free-hand  sketch  in  note  book  of  views  decided  upon. 

5.  Draw  horizontal  and  vertical  center  lines. 

6.  Lay  out  with  as  few  lines  as  possible  the  position  of  each  view. 

7.  Draw  limiting  horizontal  outlines  of  all  views. 

8.  Draw  limiting  vertical  outlines  of  all  views. 

9.  Complete  all  views. 

10.  Draw  dimension  lines. 

11.  Fill  in  dimensions. 

12.  Add  explanatory  notes,  if  required. 


Inking. — When  preparing  to  ink  a  line  do  not  overload  the  pen 
as  the  ink  is  likely  to  flow  too  freely  and  thereby  cause  a  blot.  Be 
sure,  however,  to  have  enough  ink  in  the  pen  to  finish  the  line 
about  to  be  drawn,  and  always  try  the  pen,  after  adjustment  for 
width  of  line,  on  a  piece  of  paper.  When  finished  do  not  lay  the 
pen  aside  without  cleaning. 

Fig.  15  shows  the  correct  position  of  the  ruling  pen  for  inking, 
relative  to  the  T-square,  triangle,  or  irregular  curve.  The  ruling 
pen  should  not  be  used  for  drawing  free-hand  lines. 

Sequence  for  Inking. — A  sequence  for  inking  is  more  necessary 
than  one  for  penciling,  due  to  the  necessity  of  changing  instru- 
ments and  waiting  for  ink  to  dry.  A  good  order  for  inking  is  as 
follows : 


INTRODUCTION 


11 


1.  Small  circles  and  circular  arcs  with  the  bow  pen. 

2.  Large  circles  and  circular  arcs  with  the  compass. 

3.  Irregular  curves. 

4.  Horizontal  lines  beginning  with  the  uppermost. 

5.  Vertical  lines  beginning  with  those  at  the  left-hand  end. 

6.  All  30°,  60°,  and  45°  lines. 

7.  Other  oblique  lines. 

8.  Horizontal  and  vertical  center  lines. 

9.  Extension  and  dimension  lines. 

10.  Put  in  dimensions,  arrow  heads,  and  explanatory  notes. 

11.  Section  lines. 

12.  Border  line. 

In  some  drawings  it  may  be  desirable  to  ink  center  lines  first. 

Use  of  Lines. — The  diagram  drawing  shown  in  Fig.  16  illus- 
trates the  correct  use  of  the  lines  shown  in  Fig.  3.  It  also  shows 
the  correct  and  incorrect  methods  of  forming  junctions  of  full  and 
hidden  lines  and  of  making  arrow  heads.  The  lengths  of  dashes 
and  spaces  of  broken  lines,  and  the  size  of  arrow  heads,  are  to  be 
estimated  by  eye  and  should  as  closely  resemble  those  shown  in 
Fig.  3  as  conditions  permit. 

The  drawing  of  projection  lines  is  recommended  for  all  practice 
drawings.  In  working  drawings  projection  lines  should  be 
omitted. 


FIG.  15. — Correct  position  of  ruling  pen. 

Location  of  Views. — The  amount  of  space  to  be  occupied  by 
the  title,  and  the  size  and  location  of  each  view  of  an  object  about 
to  be  drawn,  should  be  determined  before  the  drawing  is  begun. 
This  information  can  be  obtained  beforehand  by  making  a  free- 


12 


MECHANICAL  DRAWING  PROBLEMS 


hand  sketch,  preferably  in  a  note  book  kept  for  the  purpose,  and 
to  a  scale  if  necessary,  of  the  desired  views,  the  amount  of  space 
between  the  views,  and  the  distance  of  each  view  from  the  hori- 
zontal and  the  vertical  lines  comprising  the  border  line. 

In  many  cases,  if  the  drawing  is  quite  simple,  a  few  lines  drawn 
very  lightly  will  serve  as  a  preliminary  lay-out,  and  will  permit 
of  a  readjustment  of  views  should  the  first  trial  be  unsuccessful. 


/I       ,      EXTENSION  LINE 

/       M<°  y 

_4 vi-/-JJk 


INCORRECT 


DIMENSION  LINE 


PROJECTION  LINES 

+k H 




- 

x 

- 

\ 

— 

S 

«VN 

\ 

\ 

\ 

\ 

^VISIBLE  OUTLINE  ^HIDDEN  OUTLINE      AUXILIARY  LINE 
FIG.  16. — Correct  and  incorrect  junctures  of  lines. 

To  obtain  a  pleasing  appearance,  the  various  views  should  be 
arranged  and  placed  in  such  a  way  as  to  utilize  the  available 
space  on  the  sheet  to  the  best  advantage. 

Working  Drawings. — A  working  drawing,  also  called  a  shop 
drawing,  is  one  which  will  impart  such  definite  and  unmistakable 
information  in  the  form  of  a  graphic  representation  with  all  neces- 
sary dimensions,  notes  and  explanatory  matter,  the  kinds  of 
materials  to  be  used  and  methods  of  finishing,  as  is  required  by  a 
workman  for  the  construction  of  the  object  represented. 


INTRODUCTION 
GEOMETRIC  CONSTRUCTIONS 


13 


To  Bisect  a  Given  Angle  (Fig.  17). 

Let  ABC  be  the  given  angle.  With  B  as  center  and  any  suit- 
able radius  describe  arc  ab.  With  a  and  6  as  centers  and  any 
suitable  radius  describe  arcs  intersecting  at  c.  Draw  Be,  the 
bisector  of  the  angle. 


FIG.  17. 


To  Bisect  a  Given  Arc  (Fig.  18). 

Let  AB  be  the  given  arc.  With  A  and  B  as  centers  and  any 
suitable  radius  describe  arcs  intersecting  at  a.  With  A  and  B 
as  centers,  and  the  same  or  other  suitable  radius,  describe  arcs 
intersecting  at  b.  Draw  ab  intersecting  the  arc  at  c,  the  required 
point. 


I  FN 

!       i   rs 


FIG.  19. 


FIG.  20. 


To  Set  off  an  Angle  Equal  to  a  Given  Angle  from  a  Point  on  a 
Given  Line  (Fig.  19). 

Let  ABC  be  the  given  angle  and  E  the  given  point  on  line  EF . 
With  B  as  center  and  any  suitable  radius  draw  arc  ab.  From  E 
with  the  same  radius  draw  arc  cd.  With  radius  ab  and  c  as  cen- 
ter, intersect  cd  in  e.  Draw  Ee.  Then  angle  DEF  equals  angle 
ABC. 


14 


MECHANICAL  DRAWING  PROBLEMS 


To  Divide  a  Given  Line  into  Any  Number  of  Equal  Parts  (Fig. 
20). 

Let  AB  be  the  given  line,  and  six  the  required  number  of  parts. 
Draw  Ba,  at  any  angle  to  AB.  With  any  convenient  length  lay 
off  on  Ba  the  required  number  of  parts,  giving  points  6,  c,  d,  e,  f,  g. 
From  the  points  on  Ba,  and  parallel  to  gA,  draw  lines  intersecting 
A B  at  b',  c',  d',  e',  /',  giving  the  required  parts. 


FIG.  21. 


FIG.  22. 


To  Find  the  Point  of  Tangency  of  a  Given  Circular  Arc  and  a 
Given  Straight  Line  (Fig.  21). 

Let  AB  be  the  given  arc  of  center  E;  and  CD,  the  given  line. 
From  E  draw  a  perpendicular  to  CD.  The  intersection  a  will  be 
the  point  of  tangency. 


FIG.  23. 


To  Find  the  Point  of  Tangency  of  Two  Given  Circular  Arcs 
(Fig.  22). 

Let  AB  of  center  C  and  ED  of  center  F  be  the  given  arcs. 
Draw  CF.  The  intersection  a  will  be  the  point  of  tangency. 


INTRODUCTION  15 

To  Draw  an  Arc  of  Given  Radius  Tangent  to  Two  Straight 
Lines  Meeting  at  Right  Angles  (Fig.  23). 

Let  AB  and  AC  be  the  given  lines  and  R  the  given  radius. 
With  A  as  center  and  R  as  radius  draw  an  arc  intersecting  the 
given  lines  in  a  and  6.  With  a  and  6  as  centers  and  the  same 
radius  draw  arcs  intersecting  at  c.  With  c  as  center  and  the 
same  radius  draw  the  required  arc  ab.  Points  a  and  b  are  the 
points  of  tangency  of  the  arc  and  the  given  lines. 

To  Draw  an  Arc  of  Given  Radius  Tangent  to  Two  Intersecting 
Straight  Lines  (Fig.  24). 

Let  AB  and  AC  be  the  given  lines,  and  R  the  given  radius.  At 
a  distance  R  draw  parallels  to  AB  and  AC,  intersecting  at  c. 
With  c  as  center  and  radius  R  draw  the  required  arc.  Points 
a  and  b  are  the  points  of  tangency. 


FIG.  25.  FIG.  26. 


To  Draw  an  Arc  of  Given  Radius  Tangent  to  a  Given  Straight 
Line  and  a  Given  Circular  Arc  (Fig.  25). 

Let  A  B  be  the  given  line,  CD  the  given  circular  arc  of  radius 
R',  and  R  the  given  radius.  With  E  as  center  and  radius  R  +  R' 
draw  an  arc;  also  draw  a  line  parallel  to  AB  at  distance  R,  inter- 
secting the  arc  at  a.  With  a  as  center  and  radius  R  draw  the 
required  arc.  Points  b  and  c  are  the  points  of  tangency. 

NOTE. — The  point  of  tangency  b  lies  on  a  straight  line  joining  centers  a 
and  E,  and  the  point  of  tangency  c  lies  at  the  foot  of  a  perpendicular  drawn 
from  a  to  AB. 


16 


MECHANICAL  DRAWING  PROBLEMS 


To  Draw  a  Circular  Arc  Tangent  to  a  Given  Straight  Line  and 
Tangent  at  a  Point  on  a  Given  Circular  Arc  (Fig.  26). 

Let  AB  be  the  given  line  and  F  the  point  on  the  given  arc  CD 
of  radius  R.  Draw  a  line  tangent  at  F  intersecting  line  AB  at  A . 
With  A  as  center  and  radius  R'  draw  arc  ab.  With  a  and  6  as 
centers  and  radius  R"  draw  arcs  intersecting  at  c.  Draw  Ac; 
also  draw  a  straight  line  from  E  through  F  giving  point  d. 
With  d  as  center  and  radius  dF  draw  the  required  arc.  Points 
F  and  e  are  the  points  of  tangericy. 


To  Connect  Two  Given  Parallel  Lines  with  a  Compound  Curve 
and  Tangent  at  Given  Points  (Fig.  27) . 

Let  AB  and  CD  be  the  given  lines;  E  and  F  the  given  points. 
Connect  E  and  F  by  a  straight  line.  Assume  any  point,  as  G. 
Draw  ab  and  cd,  the  bisectors  of  EG  and  CrF,  respectively.  At 
E  and  F  erect  perpendiculars  giving  points  e  and  /.  With  center 
/  and  radius  R,  equal  to  /F,  draw  arc  GF.  With  center  e  and 
radius  72',  equal  to  eE,  draw  arc  GE,  completing  the  required 
curve.  Points  E  and  F  are  the  points  of  tangency.  Point  G  is 
the  point  of  tangency  of  the  two  arcs. 

To  Draw  a  Circular  Arc  of  Given  Radius  Tangent  to  Two 
Given  Circular  Arcs  (Fig.  28). 

Let  R  be  the  radius  of  the  given  arc;  and  R'  and  R"  the  radii 
of  the  given  circular  arcs.  With  E  and  F  as  centers,  and  radii 
R  +  R'  and  R  +  R",  draw  arcs  intersecting  at  a.  With  a  as 
center  and  radius  R  draw  the  required  arc.  Points  6  and  c,  on 
straight  lines  drawn  from  a  to  E  and  a  to  F,  respectively,  are  the 
points  of  tangency. 


INTRODUCTION 


17 


To  Construct  a  Regular  Polygon  of  Any  Number  of  Sides 
Within  a  Circle  of  Given  Diameter  (Fig.  29). 
Let  ABCD  be  the  given  circle.     Divide  AC  into  as  many  equal 


FIG.  29. 


parts  as  the  polygon  is  to  have  sides,  in  this  case  five.  With  A 
and  C  as  centers,  describe  arcs  of  radius  AC,  intersecting  at  a. 
A  line  drawn  through  a2,  intersecting  the  circle  at  6,  determines 


FIG.  30. 


the  length  bC,  one  side  of  the  polygon.  With  bC  as  radius  and 
b  as  center  describe  a  small  arc  giving  point  d.  The  other  points 
are  found  similarly. 


18  MECHANICAL  DRAWING  PROBLEMS 

To  Construct  a  Regular  Polygon  of  Any  Number  of  Sides  on 
a  Line  of  Given  Length  (Fig.  30). 

Let  AB  be  the  given  length.  With  B  as  center  and  A B  as 
radius  draw  the  semi-circle  A  bo.  Divide  the  semi-circle  into  as 
many  equal  parts  as  the  polygon  is  to  have  sides,  in  this  case  five. 
Draw  B2.  Bisect  AB  and  B2  to  find  the  center  of  the  circum- 
scribing circle.  Draw  lines  from  B  through  3  and  4.  The  inter- 
section of  these  lines  with  the  circumscribed  circle  determines 
the  vertices  of  the  polygon. 


A  i 


To  Draw  an  Ellipse,  the  Major  and  Minor  Axes  Being  Given 
(Fig.  31). 

Let  AB  be  the  major  axis  and  CD  the  minor  axis.  Lay  off  on 
the  edge  of  a  straight  piece  of  paper  the  distance  ac  equal  to  Ao, 
the  semi-major  axis.  Also  lay  off  the  distance  ab  equal  to  Co, 
the  semi-minor  axis.  Place  the  paper  so  that  b  coincides  with 
the  major  axis,  and  c  coincides  with  the  minor  axis,  or  the  minor 
axis  produced;  then  a  will  give  one  point  on  the  required  ellipse. 
Locate  as  many  points  as  are  necessary  to  draw  a  smooth  curve. 

To  Draw  an  Approximate  Ellipse,  the  Major  and  Minor  Axes 
Being  Given  (Fig.  32). 

Let  AB  be  the  major  axis  and  CD  the  minor  axis.  On  the 
minor  axis  lay  off  oe  and  og  equal  to  the  difference  between  the 
major  and  the  minor  axes.  On  the  major  axis  lay  off  of  and  oh 
equal  to  three-fourths  of  oe  Draw  ef,  eh,  gf,  and  gh,  all  produced. 
With  center  e  draw  arc  mDn.  With  center  g  draw  arc  kCL  With 
center/  draw  arc  kAm.  With  center  h  draw  arc  IBn,  completing 
the  required  ellipse. 


INTRODUCTION 


19 


CONVENTIONAL  SCREW  THREADS 

Screw  Threads.— Fig.  33  shows  a  method  for  drawing  conven- 
tional single  thread  screws.     Draw  two  lines  indicating  the  diam- 
eter.    On  one  line  lay  off  spaces  equal  to  the  pitch.     Bisect  one 
space  and  draw  line  ab.     From  b  draw  an  inclined  line  of  half 
b 


\  \  I  \  \  \  t 

*l  I  j—  Pitch 
J(  L_  /  Pitch 


BUTTRESS  THREAD 


M\^  Pitch 
a 


r  SHARP    V-THREAD 

FIG.  33. — Showing  steps  for  drawing  conventional  threads. 


the  pitch.  From  the  spaces  laid  off  on  one  line  draw  parallels 
to  the  inclined  line.  Complete  the  thread,  following  the  steps 
suggested  in  the  figure.  These  conventions  are  used  for  large 
screw  threads. 


FIG.  34. — Common  conventional  thread. 

For  screw  threads  under  three-quarter  inch  diameter  the  con- 
vention shown  in  Fig.  34  may  be  used.  The  spacing  for  pitch 
should  be  estimated  by  the  eye. 


20 


MECHANICAL  DRAWING  PROBLEMS 
INTERSECTION  OF  TWO   CYLINDERS 


To  Find  the  Line  of  Intersection  of  Two  Cylinders  with  Axes 
in  the  Same  Plane  and  at  Right  Angles  to  Each  Other  (Fig.  35). 

Let  A,  B,  and  C  be  the  front,  end,  and  top  views,  respectively. 
Points  on  the  line  of  intersection  may  be  found  by  the  intersection 
of  elements  in  the  surface  of  one  cylinder,  with  elements  in  the 


FIG.  35. — Intersection  by  elements  method. 

surface  of  the  other.  Let  a",  an  assumed  point,  be  the  end  view 
of  an  element,  in  the  surface  of  the  horizontal  cylinder,  which 
projected  to  the  front  and  the  top  views  gives  a'b'  and  ab,  the 
front  and  the  top  views  of  the  element.  Let  b  be  the  top  view 
of  an  element,  in  the  surface  of  the  vertical  cylinder,  which  pro- 
jected to  the  front  view  gives  c'd',  the  front  view  of  the  element. 
The  point  of  intersection  of  these  elements  gives  bf,  one  point  on 


INTRODUCTION  21 

the  required  line  of  intersection.     Additional  points  are  found 
similarly. 

The  method  of  finding  the  lines  of  intersection  of  the  hollow 
vertical  cylinder  and  the  two  holes  cut  through  its  thickness  is 
evident  from  the  figure. 

PLANE  INTERSECTION  OF  A  SOLID 

To  Find  the  Lines  of  Intersection  of  a  Surface  of  Revolution 
Cut  by  Two  Planes  at  Right  Angles  to  Each  Other  and  Parallel 
to  the  Axis  (Fig.  36). 

Let  ab  and  a'b'  be  the  projections  of  the  axis,  pp  and  p'p'  the 
end  view  of  the  cutting  planes,  and  cd  the  circular-arc  outline  of 
the  surface.  A  transverse  section  at  e,  an  assumed  point  on  the 


it  :tvt-   ± 


FIG.  36. — Intersection  by  cutting-plane  method. 


curve,  shown  in  the  end  view  as  a  circle,  is  cut  by  plane  pp.  The 
intersecting  points  of  the  circle  and  plane  projected  back  to  the 
top  view  give  //,  points  on  the  required  line  of  intersection.  A 
transverse  section  at  g,  another  assumed  point,  shown  in  the  end 
view  by  the  arc  of  a  circle,  is  cut  by  planes  pp  and  p'p'.  The 
intersecting  points  of  the  arc  and  planes  projected  back  to  the 
top  and  the  front  views  give  additional  points  on  the  line  of 
intersection.  Other  points  are  found  in  a  similar  manner. 
Through  these  points,  smooth  curves  are  drawn. 


PART  II 
EXAMPLES  AND  PROBLEMS 

DEFINITIONS 

PLANES  OF  PROJECTION 
For  example  see  Plate  5 

The  Ground  Line,  designated  in  the  drawing  as  GL,  shows  the 
division  of  two  Planes.  The  surface  above  this  line  is  called  the 
Horizontal  Plane,  or  H;  the  surface  below  the  line  is  called  the 
Vertical  Plane,  or  V. 

The  line  marked  G'U  is  called  an  Auxiliary  Ground  Line  and 
shows  the  line  of  intersection  of  the  vertical  plane  and  of  an 
Auxiliary  Horizontal  Plane. 

PROJECTIONS  ON  THREE  PLANES 

For  example  see  Plate  25 

When  drawing  three  views  of  an  object,  a  Side,  or  Profile  Plane 
is  used  in  addition  to  the  horizontal  and  vertical  planes.  The 
line  abd  is  the  ground  line,  while  the  line  cbe  is  the  Profile 
Plane  Trace.  The  surface  bounded  by  abc  is  the  horizontal 
plane.  The  surface  bounded  by  abe  is  the  vertical  plane  and  the 
surface  bounded  by  ebd  is  the  side,  or  profile  plane,  frequently 
designated  as  P. 

PROJECTIONS  ON  AUXILIARY  PLANES 
For  example  see  Plate  29 

Projections  on  Auxiliary  Planes  are  frequently  made  to  show  the 
true  shape  of  oblique  surfaces;  that  is,  of  surfaces  which  are  not 
parallel  to  any  one  of  the  regular  planes  of  projection.     Auxiliary 
planes  are  generally  perpendicular  to  H  and  inclined  to  V,  or 
perpendicular  to  V  and  inclined  to  H. 

The  surface  bounded  by  ebd  is  the  auxiliary  plane,  while  the 
line  be  is  the  Auxiliary  Plane  Trace. 

23 


24  MECHANICAL  DRAWING  PROBLEMS 


SECTION  I 

PROJECTIONS 

PRISMS 

This  drawing  shows  the  top  views,  also  called  plans,  or  hori- 
zontal projections,  and  the  front  views,  also  called  front  eleva- 
tions, or  vertical  projections,  of  four  right  prisms.  The  front 
views,  since  the  prisms  are  all  the  same  height  and  same  width, 
are  alike.  The  top  views,  which  show  their  outline  or  shape, 
cannot  be  determined  from  the  front  views;  therefore,  two  views 
are  necessary  to  represent  such  objects  completely. 

Problem  1. — Make  a  drawing  of  four  prisms  similar  to  those  shown. 
Let  A  =  3  inches,  B  =  2  inches,  and  C  =  1  inch. 

Problem  2. — Draw  top  and  front  views  of  four  prisms  similar  to  those 
shown.  Let  A  —  3J  inches,  B  =  1|  inches,  and  C  =  11  inches. 


TAPERED  OBJECTS 

This  drawing  shows  the  top  and  the  front  views  of  four  tapered 
objects.  The  front  views  are  alike  while  the  top  views  differ. 
The  first  object  is  a  wedge;  the  fourth,  a  cone. 

It  will  be  observed  that  the  front  view  of  a  wedge,  and  the 
front  view  of  a  cone  may  be  exactly  alike,  although  the  objects  are 
radically  different,  as  shown  by  their  top  views. 

Problem  1. — Draw  top  and  front  views  of  four  objects  similar  to  those 
shown.  Let  A  =  2|  inches,  B  =  1-J-  inches,  and  C  =  f  inch. 

Problem  2. — Make  a  drawing  showing  top  and  front  views  of  four  objects 
similar  to  those  shown.  Let  B  =  If  inches,  C  =  1  inch,  and  A  =  2,  2}, 
2%,  and  2f  inches,  respectively. 


PROJECTIONS 


25 
PLATE  1 


PR/SMS 

Top     Views     or    Plans     or    Horizontal      Projections 


Front     V/'ews     or    Front      Elevations    or    Vertical    Projections 


TAPERED    OBJECTS 


PLATE  2 


26 


MECHANICAL  DRAWING  PROBLEMS 


CIRCULAR  OBJECTS 

This  drawing  shows  four  circular  objects  whose  top  views  are 
alike  and  whose  front  views  vary  considerably. 

Problem  1. — Draw  top  and  front  views  of  objects  similar  to  those  shown 
and  of  the  following  dimensions: 


A 

B 

C 

D 

E 

First  object  
Second  object  
Third  object  
Fourth  object  

H 
H 

U 

H 

I 

3 
3i 
3i 
3f 

a 

H 
H 

1 

'j 

Problem  2. — Draw  top  and  front  views  of  objects  similar  to  those  shown 
and  of  the  following  dimensions : 


A 

B 

C 

D 

E 

First  object 

If 

1 

gJL 

Second  object  

ill 

if 

3& 

7 

Third  object  
Fourth  object 

H 
1H 

1 

IjL 

3A 
3^ 

i& 

if 

H 

GEOMETRIC  OBJECTS 

This  drawing  shows  four  objects  whose  top  views  are  similar 
but  whose  front  views  differ. 

Problem  1. — Make  a  drawing  showing  top  and  front  views  of  objects 
similar  to  those  shown  and  of  the  following  dimensions: 


A 

B 

C 

D 

E 

F 

G 

H 

First  object  
Second  object.... 
Third  object  
Fourth  object.... 

H 
If 
H 
If 

31 
34 
8| 

3 

1 
I 
f 

1 

H 
U 
11 

H 

1\ 
\ 
\ 
1 

2J 

1 

If 

U 

Problem  2. — Make  a  drawing  showing  top  and  front  views  of  objects 
similar  to  those  shown  and  of  the  following  dimensions : 


A 

B 

C 

D 

# 

F 

G 

H 

First  object  

U 

3$ 

1 

U 

2i 

Second  object.... 

U 

Si 

f 

M 

I 

2 

Third  object  

If 

31 

f 

U 

Itt 

Fourth  object.... 

1J 

84 

i 

H 

i 

1 

2| 

2H 

PROJECTIONS 


27 
PLATE  3 


CIRCULAR   OBJECTS 


UsJ 


GEOMETRIC   OBJECTS 


1 

•  f 

1 

UJ 

f 

iJJ 

1 

O 

-4' 

Ul 

f 

i 

i 

PLATE 


28 


MECHANICAL  DRAWING  PROBLEMS 


GEOMETRIC  OBJECT 

This  drawing  shows  the  top  and  the  front  views  of  an  object 
in  three  positions  in  relation  to  GL. 

The  top  views  show  the  object  in  contact  with  GL,  therefore 
in  contact  with  V.  See  page  23. 

Problem  1. — Draw  top  and  front  views  of  the  object  in  positions  similar 
to  those  shown  and  of  the  following  dimensions : 


A 

B 

c 

D 

B 

e 

4> 

First  position  

2 

If 

2f 

t 

A 

Second  position  

2 

H 

3 

! 

A 

30°    | 

Third  position  

2 

ii 

31 

I 

A 

45° 

Problem  2. — Make  a  drawing  showing  top  and  front  views  of  the  object 
in  positions  similar  to  those  shown  and  of  the  following  dimensions : 


A 

B 

C 

.,    ...  . 
D          E 

e         <t> 

First  position  

n 

H 

2f 

A 

i 

Second  position  

2 

U 

3 

1 

A 

15° 

Third  position  

2| 

if 

31 

A 

t 

45° 

GEOMETRIC  SOLID 

This  drawing  shows  the  top  and  the  front  views  of  a  triangular 
solid  in  three  positions. 

Problem  1. — Draw  top  and  front  views  of  a  similar  solid  having  the  fol- 
lowing dimensions  and  positions : 


A 

B 

C 

D 

E 

e 

0 

First  position  

2J 

If 

2* 

11 

* 

Second  position  

2| 

U 

3 

U 

1 

45° 

Third  position  

2| 

If 

3| 

U 

H 

30° 

Problem  2. — Make  a  drawing  showing  top  and  front  views  of  a  similar 
solid  having  the  following  dimensions  and  positions : 


A 

B 

C 

D 

E 

e 

<t> 

First  position  
Second  position  
Third  position  

21 
2| 
2} 

2 
11 
If 

BJ 

3 
21 

1! 

If 

1 

f 
f 

15° 

75° 

PROJECTIONS 


29 
PLATE  6 


GEOMETRIC   OBJECT 


Position 


Second  Position 


Third  Position 


GEOMETRIC    SOLID 


PLATE  6 


30 


MECHANICAL  DRAWING  PROBLEMS 


PROJECTION  OF  LETTER  (V) 

This  drawing  shows  the  top  and  the  front  views  of  a  letter  con- 
sisting of  horizontal,  vertical,  and  oblique  lines,  in  three  positions 
relative  to  V. 

In  solving  the  following  problems  draw  the  front  view  of  the 
letter  in  its  first  position  and  project  the  top  view.  Transpose  the 
top  view  to  the  required  positions  and  project  the  front  views. 

Problem  1. — For  the  first  position,  draw  the  front  view  of  the  letter  as 
shown;  project  the  top  view  when  removed  one  inch  from  V.  For  the  second 
position,  let  one  corner  be  in  contact  with  V ,  and  6  =  30°.  For  the  third 
position  show  the  nearest  corner  removed  £  inch  from  V,  and  <f>  =  15°. 

Problem  2. — Draw  front  and  top  views,  as  explained  in  Problem  1, 
when  the  letter  is  inverted.  Insert  a  cross-bar  and  change  the  letter  to  A. 
Show  hidden  lines  in  the  front  view  of  the  third  position. 


PROJECTION  OF  LETTER  (K) 

This  drawing  shows  the  top  and  the  front  views  of  a  letter  con- 
sisting of  horizontal,  vertical,  and  oblique  lines  in  three  positions. 

For  drawing  the  following  problems  read  the  instructions  given 
for  letter  V. 

Problem  1. — Draw  front  and  top  views  in  positions  similar  to  those  shown 
and  of  the  following  dimensions : 


A 

B 

C 

D 

E 

F 

G 

e 

<t> 

3f 

3i 

3 

i 

1 

I 

2| 

30' 

45° 

Show  all  hidden  lines  in  the  front  view  of  the  second  position. 

Problem  2. — Using  the  letter  K  as  a  guide,  design  the  letter  X  and  draw 
views  in  positions  similar  to  those  shown  for  K  and  of  general  dimensions, 
as  follows: 


A 

B 

C 

D            E 

F 

G 

e 

* 

3i 

3| 

n 

1     \    - 

i 

2J 

15° 

30° 

Show  all  hidden  lines  in  the  front  view  of  the  third  position. 


PROJECTIONS 


31 
PLATE  7 


PROJECTION  OF  LETTER 


PROJECTION   or  LETTER 


PLATE  8 


32  MECHANICAL  DRAWING  PROBLEMS 

HOLLOW  CYLINDER 

This  drawing  shows  the  top  and  the  front  views  of  a  hollow 
cylinder  in  three  positions. 

For  the  first  position,  draw  front  and  top  views  as  shown. 
Divide  the  front  view,  giving  points  1',  2',  3',  etc.  Project  these 
points  to  the  top  view.  For  the  second  and  the  third  positions, 
transpose  the  top  view  and  locate  points  for  the  front  views  by 
projecting  lines  as  shown. 

Problem  1. — Draw  the  cylinder  in  positions  similar  to  those  shown  and 
having  the  following  dimensions : 


A 

B 

c 

e 

<p 

3 

H 

H 

30° 

60° 

Complete  the  second  view  and  show  hidden  lines. 

Problem  2. — Draw  the  cylinder  in  positions  similar  to  those  shown  and 
having  the  following  dimensions : 


Complete  the  second  view  and  show  hidden  lines  in  the  third  position. 
GEOMETRIC  SOLID 

This  drawing  shows  the  top  and  the  front  views  of  a  solid  in 
three  positions. 

Problem  1. — Draw  top  and  front  views  of  the  solid  in  positions  similar 
to  those  shown  and  having  the  following  dimensions: 


A 

B 

C 

D 

E 

e 

<t> 

2 

2| 

3i               If 

1 

30° 

45° 

Complete  the  second  view  and  show  hidden  lines. 

Problem  2. — Draw  views  similar  to  those  shown  when  the  solid  has  the 
following  dimensions : 


A 

B 

C 

D 

E 

e             <t> 

U 

2| 

2H 

ii 

1 

15°              75° 

Complete  the  second  view  and  show  hidden  lines  in  the  third  position. 


PROJECTIONS 


33 
PLATE 


HOLLOW    CYLINDER 


GEOMETRIC  SOLID 


PLATE  10 


34 


MECHANICAL  DRAWING  PROBLEMS 


PROJECTION  OF  LETTER  (P) 

This  drawing  shows  the  top  and  the  front  views  of  the  letter 
P  in  three  positions. 

For  the  first  position,  draw  front  and  top  views  as  shown. 
Divide  the  circular  arc,  whose  center  is  to  be  found  by  trial,  into 
any  number  of  parts,  and  project  the  points  found  to  the  top  view. 
Transpose  the  top  view  to  the  second  and  third  positions  and 
project  the  front  views. 

Problem  1. — Draw  similar  positions  of  the  letter  with  the  following 
dimensions: 


A 

B 

C 

D 

E 

F 

G 

TT 

e 

<t> 

3f 

1 

3 

li 

f 

1 

21 

u 

30° 

60° 

Show  all  hidden  lines  in  the  front  view  of  the  second  position. 

Problem  2. — Draw  similar  positions  of  the  letter  when  transformed  into 
the  letter  R  with  the  following  dimensions : 


A 

B 

C     \     D 

E 

F 

G 

H 

; 

<£ 

3| 

I 

21         1* 

tt 

A 

21 

1A 

15° 

45° 

Show  all  hidden  lines  in  the  front  view  of  the  third  position. 

PROJECTION  OF  LETTER  (S) 

This  drawing  shows  the  front  and  the  top  views  of  the  letter  S 
in  three  positions. 

For  the  first  position,  draw  front  and  top  views  as  shown. 
Assume  points  on  the  circular  arcs  of  the  front  view  and  project 
these  points  to  the  top  view.  Transpose  the  top  view  to  the 
second  and  third  positions  and  project  the  front  views. 

Problem  1. — Draw  the  letter  in  the  three  positions  having  the  dimensions 
shown.  Let  6  =  30°,  and  <f>  =  45°. 

Problem  2. — For  the  first  position,  draw  the  front  view  as  shown  and  pro- 
ject the  top  view  when  removed  one  inch  from  V.  For  the  second  position, 
turn  the  top  view  in  a  counterclockwise  direction  to  an  angle  of  30°  with  V. 
For  the  third  position,  turn  the  top  view  in  a  clockwise  direction  to  an  angle 
of  45°  with  V.  Let  a  point  of  the  letter  be  in  contact  with  V  in  the  second 
and  the  third  positions. 


PROJECTIONS 


35 
PLATE  11 


PROJECTION  or  LETTER 


PROJECTION  or  LETTER 


PLATE  12 


36  MECHANICAL  DRAWING  PROBLEMS 


ANGLES  GREATER  THAN  90  DEGREES 

Angles  greater  than  90  degrees,  as  called  for  in  Problem  2  in 
each  of  the  six  following  drawings,  are  drawn  with  the  triangles. 
To  draw  an  angle  greater  than  90  degrees  draw  its  supplement, 
which  is  the  difference  between  the  required  angle  and  180  de- 
grees, or  straight  angle. 

PRISMS 

To  find  the  projections  of  a  right  prism  when  inclined  to  the 
horizontal  and  the  vertical  planes  of  projection. 

Draw  the  top  and  the  front  views  as  shown  for  the  first  posi- 
tion. Transpose  the  front  view  to  the  second  position,  turning  it 
through  the  required  angle,  and  project  the  top  view.  Transpose 
the  top  view  to  the  third  position,  turning  it  through  the  required 
angle,  and,  finally,  find  the  front  view. 

TRIANGULAR  PRISM 
Eqtulateral  Base 

Problem  1. — Draw  top  and  front  views  of  the  prism  in  positions  similar 
to  those  shown.  Let  A  =  2  inches,  B  =  3  inches,  6  =  30°,  and  4>  =  45°. 

Problem  2. — Draw  top  and  front  views  for  the  first  position,  when  the 
prism  is  turned  about  its  central  vertical  axis  through  an  angle  of  180°. 
Let  A  =  If  inches  and  B  =  2f  inches. 

Find  the  front  views  when  the  top  views  are  turned  about  df.  Let  6  = 
135°,  $  =  150°,  and  d  be  in  contact  with  V  for  the  third  position. 


PENTAGONAL  PRISM 
Regular  Base 

Problem  1. — Draw  top  and  front  views  of  the  prism  in  positions  similar 
to  those  shown.  Let  A  =  1J  inches,  B  =  3  inches,  6  =  60°,  and  <f>  =  45°. 

Problem  2. — Draw  top  and  front  views  for  the  first  position,  when  the 
prism  is  turned  about  its  central  vertical  axis  through  an  angle  of  180°. 
Let  A  =  \\  inches,  B  =  2f  inches. 

Find  the  front  views  when  the  top  views  are  turned  about  Cidi.  Let 
e  =  135°,  <t>  =  150°,  and  &  be  in  contact  with  V  for  the  third  position. 


PROJECTIONS 


37 
PLATE  13 


TRIANGULAR    PRISM 

EQUILATERAL     BASE 


PENTAGONAL  PRISM 

REGULAR    BASE 


PLATE  14 


38  MECHANICAL  DRAWING  PROBLEMS 


PYRAMIDS 

To  find  the  projections  of  a  pyramid  when  resting  on  one  corner 
of  its  base,  and  inclined  to  the  horizontal  and  the  vertical  planes. 

Draw  the  top  view,  making  any  desired  angle  with  GL,  and 
find  the  front  view.  Transpose  the  front  view,  turning  it 
through  the  required  angle,  and  draw  the  top  view.  Transpose 
the  top  view,  turning  it  through  the  required  angle,  and,  finally, 
find  the  front  view. 

SQUARE  PYRAMID 

Problem  1. — Draw  top  and  front  views  of  the  pyramid  in  positions  similar 
to  those  shown.  Let  A  =  2  inches,  B  =  3j  inches,  <*  =  20°,  6  =  45°,  and 
<t>  =  30°. 

Problem  2. — Draw  top  and  front  views  of  the  pyramid  when  inclined 
to  H  and  V  and  resting  on  a  corner  of  its  base.  Let  A  =  If  inches,  B  =  3 
inches,  <*  =  15°,  0  =  120°,  <f>  =  150°,  and  let  a  corner  of  its  base  be  in  con- 
tact with  V. 


HEXAGONAL  PYRAMID 
Regular  Base 

Problem  1. — Draw  top  and  front  views  of  the  pyramid  when  inclined  to 
H  and  V  and  resting  on  a  corner  of  its  base.  Let  A  =  1  inch,  B  =  3J 
inches,  0  =  45°,  and  <f>  =  60°. 

Problem  2. — Draw  top  view  of  the  pyramid  for  the  first  position,  when 
turned  counterclockwise  about  /  through  an  angle  of  30°,  and  project  front 
view.  Let  A  =  1$  inches  and  B  =  3|  inches.  Find  top  and  front  views 
when  turned  about  one  edge  of  its  base  resting  on  H.  Let  6  =  120°,  <f>  = 
135°,  and  let  a  corner  of  the  base  be  in  contact  with  V. 


PROJECTIONS 


39 
PLATE  16 


SQUARE    PYRAMID 


HEXAGONAL   PYRAMID 

REGULAR   BASE: 


a'   ftl     \ 


PLATE  16 


40  MECHANICAL  DRAWING  PROBLEMS 


CONE  AND  CYLINDER 

To  find  the  projections  of  a  cone  or  a  cylinder  with  its  axis 
inclined  to  the  horizontal  and  the  vertical  planes. 

Draw  the  top  and  the  front  views  of  the  cylinder  or  the  cone. 
Divide  the  top  view  into  equal  parts  as  shown,  and  project  to  the 
front  view.  Transpose  the  front  view,  turning  it  through  a 
required  angle,  and  proj  ect  the  top  view .  Transpose  the  top  view, 
turning  it  through  a  required  angle,  and,  finally,  project  the 
front  view. 

RIGHT  CONE 

Problem  1. — Draw  top  and  front  views  of  a  right  cone  when  resting  on  a 
point  of  its  base  and  inclined  to  H  and  V.  Let  A  —  2  inches,  B  =  3| 
inches,  9  =  45°,  and  <f>  =  45°. 

Problem  2. — Draw  top  and  front  views  of  a  right  cone  when  resting  on  a 
point  of  its  base  and  inclined  to  H  and  V.  Let  A  =  If  inches,  B  =  3i 
inches,  6  =  135°,  and  <j>  =  135°. 


RIGHT  CYLINDER 

Problem  1. — Draw  top  and  front  views  of  a  right  cylinder  when  resting 
on  a  point  of  its  base  and  inclined  to  H  and  V.  Let  A  =  2  inches,  B  =  3 
inches,  6  =  45°,  and  <f>  =45°. 

Problem  2. — Draw  top  and  front  views  of  a  right  cylinder  when  resting 
on  a  point  of  its  base  and  inclined  to  H  and  V.  Let  A  =  1  j  inches,  B  =  2J 
inches,  0  =  135°,  and  <j>  =  135°. 


PROJECTIONS 


41 
PLATE  17 


RIGHT    CONE 


b          c'1      2' 


RIGHT    CYLINDER 


PLATE  18 


42  MECHANICAL  DRAWING  PROBLEMS 


SQUARE  PRISMS 

To  draw  the  projections  of  a  square  prism  resting  on  the  edge  of 
another  square  prism. 

Draw  the  front  view  as  shown  in  the  first  position  and  project 
the  top  view.  Transpose  the  top  view  to  the  second  position, 
turning  it  through  a  required  angle.  The  front  view  of  the  second 
position  is  then  found  by  projecting  from  the  top  view  of  the 
second  position  and  the  front  view  of  the  first  position. 

Problem  1. — Find  the  front  view  of  the  two  prisms  when  6  —  30°  and 
</>  =  45°. 

Problem  2. — Find  the  front  view  of  the  two  prisms  when  the  top  view  of 
the  second  position  is  turned  in  a  clockwise  direction  through  an  angle  of 
30°.  instead  of  counterclockwise  as  shown.  Let  6  =  30°. 


CROSS  AND  PRISM 

To  draw  the  projections  of  a  cross  and  a  prism  with  one  edge  of 
the  former  resting  on  the  latter. 

Draw  the  front  view,  as  shown  in  the  first  position,  and  project 
the  top  view,  including  all  hidden  lines,  and  proceed  as  explained 
for  SQUARE  PRISMS. 

Problem  1. — Find  the  front  view  of  the  cross  and  the  prism  when  6  =  60° 
and  <t>  =  30°.  Determine  the  height  of  the  prism  by  measurement. 

Problem  2. — Find  the  front  view  of  the  cross  and  the  prism  when  the 
top  view  of  the  second  position  is  turned  in  a  counterclockwise  direction 
through  an  angle  of  45°,  instead  of  clockwise  as  shown.  Let  6  =  75°. 
Determine  the  height  of  the  prism  by  measurement. 


PROJECTIONS 


43 
PLATE  19 


SQUARE    PHI  SMS 


CROSS  AND  PRISM 


PLATE  20 


44  MECHANICAL  DRAWING  PROBLEMS 


LETTER  AND  PRISM  (Z) 

To  draw  the  projections  of  a  letter  resting  on  an  edge  of  a 
triangular  prism. 

Draw  the  front  view  and  project  the  top  view,  showing  all 
hidden  lines.  If  the  letter  contains  curved  lines  it  will  be  neces- 
sary to  assume  a  number  of  points  in  the  front  view  and  project 
these  points  to  the  top  view,  as  shown  by  points  1  and  2  in  the 
letter  R.  Transpose  the  top  view  to  the  second  position,  turning 
it  through  a  required  angle,  and  find  the  front  view. 

Problem  1. — Design  the  letter  H,  of  the  same  general  dimensions  and 
position  as  shown  for  the  letter  Z,  and  find  the  front  view  when  both  letter 
and  prism  are  inclined  to  F.  Let  8  =  30°  and  <j>  =  60°. 

Problem  2. — Draw  the  front  view  of  the  letter  shown  when  moved  over 
the  prism  toward  the  left,  until  the  left  edge  rests  on  the  auxiliary  horizontal 
plane,  and  the  right  end  rests  on  the  prism,  and  when  both  are  inclined  to 
V.  Let  the  bottom  of  the  letter  be  inclined  30°  to  H,  and  <t>  =  120°. 


LETTER  AND  PRISM  (R) 

Problem  1. — Find  the  front  view  of  the  letter  and  the  prism  when  the 
top  view  of  the  second  position  is  turned  in  a  counterclockwise  direction, 
instead  of  clockwise  as  shown.  Let  6  =  30°  and  tf>  =  120°.  The  height  of 
the  prism  is  to  be  found  by  measurement. 

Problem  2. — Find  the  front  view  when  the  letter  is  moved  over  the  prism 
toward  the  right,  until  the  right  edge  rests  on  the  auxiliary  horizontal  plane, 
and  the  left  end  rests  on  the  prism,  and  when  both  are  inclined  to  V.  Let 
the  bottom  of  the  letter  be  inclined  30°  to  H,  and  $  =  60°.  The  height  of 
the  prism  is  to  be  found  by  measurement. 


PROJECTIONS 


45 
PLATE  21 


LETTER   AND  PRISM 


LETTER  AND  PRISM 


PLATE  22 


46 


MECHANICAL  DRAWING  PROBLEMS 


CYLINDER  AND  PRISM 

To  draw  the  projections  of  an  inclined  cylinder  resting  on  an 
edge  of  a  triangular  prism. 

Draw  the  front  view  and  project  the  top  view.  Transpose  the 
top  view  to  the  second  position,  turning  it  through  a  required 
angle,  and  project  the  front  view. 

The  ends  of  the  cylinder  in  the  top  view  of  the  first  position 
are  found  by  dividing  the  surface  of  the  cylinder,  by  aid  of  aux- 
iliary half-circles,  in  both  views,  into  a  number  of  equal  parts  as 
shown. 

Problem  1. — Find  the  front  view  of  the  cylinder  and  the  prism  when 
both  are  inclined  to  V  and  of  the  following  dimensions: 


J 

B 

C 

D 

E 

e 

<i> 

It 


II 


45° 


15C 


Omit  hidden  lines  in  the  second  position. 

Problem  2. — Find  the  front  view  of  the  cylinder  and  prism  when  both  are 
inclined  to  V  and  of  the  following  dimensions: 


A                B 

C 

D 

\ 

3i                 2}               If 

11 

2* 

135° 

30° 

Cylinder  will  be  on  the  right  side  of  the  prism  instead  of  on  the  left  as 
shown.     Show  all  hidden  lines. 

CONE  AND  CYLINDER 

Problem  1. — Find  the  front  view  of  the  cone  and  the  cylinder  when 
both  are  inclined  to  V  and  of  the  following  dimensions: 


41 


45° 


30° 


Show  all  hidden  lines. 

Problem  2. — Find  the  front  view  of  the  cone  and  the  cylinder  when  both 
are  inclined  to  V  and  of  the  following  dimensions : 


B 


135C 


30° 


Cone  will  be  on  the  left  side  of  the  cylinder  instead  of  on  the  right  as 
shown.     Show  all  hidden  lines. 


PROJECTIONS 


47 
PLATE  23 


CYLINDER  AND    PRISM 

1 


CONE  AND  CYLINDER 


PLATE  24 


48  MECHANICAL  DRAWING  PROBLEMS 


PROJECTIONS  ON  THREE  PLANES 

The  four  following  drawings  show  the  top  view,  the  front  view, 
and  the  side  view  of  simple  objects.  See  page  23. 

The  side  view  of  an  object  is  generally  shown  on  the  right  side 
of  the  front  view.  It  may,  however,  be  shown  on  the  left  side,  if 
some  special  features  of  the  object  warrant  the  change. 

PROJECTION  PROBLEMS 

(First  Drawing) 

Problem  1. — Draw  three  views  of  the  first  figure  when  turned  about  its 
central  vertical  axis  from  the  position  shown,  through  an  angle  of  180°. 

Draw  three  views  of  the  second  figure  when  turned  about  its  central  ver- 
tical axis  from  the  position  shown,  through  an  angle  of  180°.  Let  6  =  30°. 

Assume  distances  from  H,  V,  and  P,  for  both  figures. 

Problem  2. — Draw  three  views  of  the  first  figure  when  turned  through  an 
angle  of  90°  about  its  central  vertical  axis  in  a  clockwise  direction. 

Draw  three  views  of  the  second  figure  when  6  =  135°. 

Assume  distances  from  H,  V,  and  P,  for  both  figures. 


PROJECTION  PROBLEMS 
(Second  Drawing) 

Problem  1. — Draw  three  views  of  the  first  figure  in  the  position  shown, 
/mitting  the  rectangular  hole. 

Draw  three  views  of  the  second  figure,  including  the  hole,  when  6  =  60°. 

Problem  2. — Draw  three  views  of  the  first  figure  when  turned  about  its 
central  vertical  axis  through  an  angle  of  90°. 

Draw  three  views  of  the  second  figure  when  0  =  135°. 


PROJECTIONS 


49 
PLATE  26 


Top    View 

Plan  |c 


Horizontal  Proj. 


PROBLEMS 

FIRST     DRAWING 


Top  Wew 


Front  Elevation      Side  Elevation 
Vertical  Proj.        Profile  Proj. 


VH~^  \      \ 

d-L  \\  \ 

>   >      • 


Fronf  Wew     e      5/c/e  Wew 


PROJECTION     PROBLEMS 

SECOND     DRAWING 


PLATE  26 


50  MECHANICAL  DRAWING  PROBLEMS 

PROJECTIONS  ON  THREE  PLANES 
(Continued) 

In  many  cases  a  figure  may  be  completely  shown  by  two  views, 
but  if  three  views  will  show  its  construction  more  clearly,  then 
three  views  are  given.  The  figures  in  the  drawings  on  page  49 
are  completely  shown  by  the  front  and  the  side  views  alone,  but 
the  addition  of  the  top  views  gives  a  greater  degree  of  clearness 
to  their  form. 

A  close  study  of  the  figures  of  the  third  and  fourth  drawings  of 
PROJECTION  PROBLEMS  shows  that  two  views  of  any  one  figure  are 
insufficient  for  its  complete  representation. 

PROJECTION  PROBLEMS 
(Third  Drawing) 

Problem  1. — Draw  three  views  of  the  first  figure  when  removed  |  inch 
from  V,  |  inch  from  H,  and  i  inch  from  P. 

Draw  three  views  of  the  second  figure  when  removed  i  inch  from  V, 
|  inch  from  H,  and  j  inch  from  P. 

Problem  2. — Draw  three  views  of  the  first  figure  when  turned  through 
an  angle  of  180°  about  its  vertical  axis.  Let  the  figure  be  removed  i  inch 
from  V,  f  inch  from  H,  and  j  inch  from  P. 

Draw  three  views  of  the  second  figure  when  turned  through  an  angle  of 
90°  about  its  vertical  axis.  Let  the  figure  be  removed  |  inch  from  V,  I 
inch  from  H,  and  f  inch  from  P. 

PROJECTION  PROBLEMS 

(Fourth  Drawing) 

Problem  1. — Draw  three  views  of  the  first  figure  when  removed  f§,  I, 
and  f  inches  from  V,  H,  and  P,  respectively. 

Draw  three  views  of  the  second  figure  having  its  central  vertical  axis 
1J  inches  from  both  V  and  P.  Let  the  figure  rest  on  an  auxiliary  H  plane 
which  is  4f  inches  from  H. 

Problem  2. — Draw  three  views  of  the  first  figure  when  turned  about  its 
central  vertical  axis  through  a  half-revolution.  Let  the  axis  be  £  inch 
from  V,  1|  inches  from  P,  and  let  the  top  of  the  figure  be  f  inch  below  H. 

Draw  three  views  of  the  second  figure  when  turned  about  its  central 
vertical  axis  through  a  quarter-revolution  in  a  counterclockwise  direction. 
Let  the  axis  be  1^  inches  from  V,  l\  inches  from  P,  and  let  the  top  of  the 
figure  be  f  inch  below  H. 


PROJECTIONS 


51 
PLATE  27 


PROJECTION     PROBLEMS 

THIRD    DRAW/NO 


PROJECTION     PROBLEMS 

FOURTH     DRAWING 


PLATE  28 


52 


MECHANICAL  DRAWING  PROBLEMS 


PROJECTION  PROBLEMS 
(Fifth  Drawing) 

See  page  23 

Problem  1. — Draw  front,  top,  and  auxiliary  views  with  the  following 
dimensions : 


A 

B 

C 

D 

e 

First  Figure 

2J 

If 

li 

i 

30° 

Second  Figure 

2| 

1 

1 

60° 

Problem  2. — Draw  front,  top,  and  auxiliary  views  with  the  following 
dimensions : 


A 

B 

C 

D 

e 

First  Figure 

2f 

U 

H 

i 

30° 

Second  Figure  

2| 

U 

0 

45° 

PROJECTION  PROBLEMS 

(Sixth  Drawing) 

Problem  1. — Draw  four  views  of  each  object  in  positions  similar  to  those 
shown  and  of  the  following  dimensions: 


A 

B 

C 

e 

First  Figure  

1\ 

If 

If 

60° 

Second  Figure 

31 

1 

2 

45° 

Show  all  hidden  lines  in  both  objects. 

Problem  2. — Draw  four  views  of  each  of  the  two  objects  using  the  follow- 
ing dimensions: 


A 

B 

C 

e 

First  Figure  

si 

If 

H 

45° 

Second  Figure 

31 

1 

2 

45° 

The  first  object  is  to  be  turned  about  its  central  vertical  axis  through  an 
angle  of  180°;  the  second,  to  be  turned  about  its  central  vertical  axis  in  a 
clockwise  direction  through  an  angle  of  90°.  See  second  paragraph  page  48. 

Show  all  hidden  lines  in  both  objects. 


PROJECTIONS 


53 
PLATE  29 


PROJECTION     PROBLEMS 

FIFTH    DRAWING 


Top  View 


Front   View 


PROJECTION    PROBLEMS 

SIXTH    DRAWING 


Auxiliary    View 
Top  View  ,•*- 


Front    View  Side    View 


PLATE  30 


54  MECHANICAL  DRAWING  PROBLEMS 

SECTION  II 
DEVELOPMENTS  AND  INTERSECTIONS 

DEVELOPMENT 

The  shape  of  the  surface  of  an  object  when  laid  out  on  a  plane 
is  its  development,  or  pattern. 

In  the  developments  of  the  following  drawings,  the  overall  di- 
mensions, a  number  of  which  are  not  shown,  although  the  dimen- 
sion lines  are  drawn,  are  to  be  found  by  accurately  measuring  the 
drawing. 

RECTANGULAR  PRISM 

To  find  the  development  of  a  rectangular  prism,  first  draw  top 
and  front  views  of  the  object.  Then  draw  a  horizontal  line  of 
indefinite  length  and  lay  off  distances  equal  to  the  lengths  of  the 
lateral  faces  as  found  from  the  top  view.  At  these  points  erect 
vertical  lines,  and  measure  off  the  lengths  of  the  lateral  edges  as 
found  from  the  front  view.  Complete  the  lateral  area,  or  surface, 
by  drawing  a  line  connecting  the  heights  of  the  edges. 

Problem  1. — Draw  top  and  front  views,  and  find  the  development  of  a 
prism  having  a  base  of  li  X  If  inches  and  a  height  of  2f  inches. 

Problem  2. — Draw  top  and  front  views,  and  find  the  development  of  a 
prism  having  a  base  of  If  X  2|  inches  and  a  height  of  2i  inches.  In  the 
projections  show  the  narrow  faces  of  the  prism  parallel  to  V. 

REVOLVED  SURFACE 

A  revolved  surface  is  a  projection  which  shows  the  true  shape  of 
the  face  of  an  object  which  is  not  parallel  to  the  regular  planes  of 
projection. 

TRUNCATED  RECTANGULAR  PRISM 

To  find  the  development  of  a  truncated  rectangular  prism,  first 
draw  top  and  front  views  and  the  revolved  surface  of  the  object. 
Then  draw  the  lateral  surface,  the  length  being  equal  to  the 
perimeter  of  the  top  view,  and  the  several  heights  being  equal  to 
the  lateral  edges  found  from  the  front  view. 

Problem  1. — Draw  two  views,  the  revolved  surface,  and  find  the  develop- 
ment of  a  truncated  prism  having  a  If-inch  square  base  and  a  height  of  3 
inches.  Let  the  angle  in  the  front  view  be  30°  with  a  horizontal. 

Problem  2. — Draw  two  views,  the  revolved  surface,  and  find  the  develop- 
ment of  a  truncated  prism  having  a  base  of  li  X  2i  inches  and  a  height  of 
2f  inches.  In  the  projections  show  the  narrow  faces  parallel  to  V.  Assume 
suitable  angle  for  the  inclined  surface. 


DEVELOPMENTS  AND  INTERSECTIONS  55 

PLATE  31 


RECTANGULAR    PRISM 


Top  View 


TRUNCATED 

RECTANGULAR  PRI6M 


Front  View 


PLATE  32 


56  MECHANICAL  DRAWING  PROBLEMS 


TRIANGULAR  WEDGE 

To  find  the  development  of  a  triangular  object,  like  the  wedge 
shown  in  the  drawing,  first  draw  top  and  front  views.  Lay  out  a 
rectangular  surface  whose  height  equals  the  height  of  the  wedge 
and  whose  length  equals  the  perimeter  of  the  top  view.  To  this 
rectangular  surface  attach  triangular  surfaces  equal  to  the  top 
and  the  bottom  of  the  wedge. 

The  true  lengths  of  the  sides  of  the  wedge  may  be  found  by  cal- 
culation, or  by  measurement  of  the  top  view. 

Problem  1. — Draw  two  views,  and  the  developed  surface  of  a  triangular 
wedge.  Reduce  the  horizontal  dimensions,  shown  in  the  drawing,  J  inch 
and  increase  the  vertical  dimension  f  inch. 

Problem  2. — Draw  top  and  front  views  of  the  triangular  wedge,  shown  in 
the  drawing,  when  turned  about  its  central  vertical  axis  through  a  half 
revolution.  Develop  the  surface  when  opened  on  the  edge  ad,  instead  of 
be  as  shown. 


TRUNCATED  SQUARE  PRISM 

To  find  the  development  of  a  truncated  prism  similar  to  that 
shown,  first  draw  top  and  front  views  and  the  revolved  surface. 
Lay  out  the  lateral  surface,  the  length  being  found  from  the  top 
view  and  the  several  heights  being  found  from  the  front  view. 
Attach  surfaces  equal  to  the  revolved  and  the  bottom  surfaces. 

Problem  1. — Draw  top  and  front  views,  the  revolved  surface,  and  the 
development  of  the  prism,  when  the  60°  angle  shown  in  the  front  view  is 
changed  to  45°. 

Problem  2. — Draw  two  views,  and  the  revolved  surface,  as  shown  in  the 
drawing,  and  find  the  development  when  opened  on  the  line  ab. 


DEVELOPMENTS  AND  INTERSECTIONS  57 
PLATE  33 

TRIANGULAR    WEDGE 


TRUNCATED    SQUARE  PRISM 

(9, 


Revolved 
Surface   ,-" —•* 


PLATE  34 


58  MECHANICAL  DRAWING  PROBLEMS 


[TRUNCATED  TRIANGULAR  PRISM 

To  find  the  development  of  a  triangular  prism  similar  to  that 
shown,  draw  top  and  front  views,  and  the  revolved  surface.  Lay 
out  the  lateral  surface.  Attach  triangular  surfaces  equal  to  the 
revolved  and  the  bottom  surfaces. 

Problem  1. — Draw  top  and  front  views,  the  revolved  surface,  and  the 
development  when  the  45°  angle  in  the  front  view  is  changed  to  60°.  Show 
development  when  opened  on  the  shortest  edge  of  the  prism. 

Problem  2. — Draw  the  top  view,  when  revolved  through  an  angle  of 
180°  about  its  center,  and  project  the  front  view.  Let  the  front  view  of  the 
inclined  surface  be  as  shown.  Project  the  revolved  surface  and  find  develop- 
ment when  opened  on  one  of  the  shortest  edges  of  the  prism. 


TRUNCATED  HEXAGONAL  PRISM 

To  find  the  development  of  an  hexagonal  prism  similar  to  that 
shown,  draw  top  and  front  views,  and  the  revolved  surface;  then 
proceed  as  explained  for  the  triangular  prism. 

Problem  1. — Draw  top  and  front  views  of  the  prism  showing  the  inclined 
surface  beginning  at  a',  in  the  front  view,  and  making  an  angle  of  30°  with 
the  horizontal.  Project  the  revolved  surface  and  find  the  development 
when  opened  on  the  shortest  edge  of  the  prism. 

Problem  2. — Draw  top  and  front  views  of  the  prism  when  turned  about 
its  central  vertical  axis  through  an  angle  of  30°.  Let  the  inclined  surface 
in  the  front  view  begin  at  the  axis  and  make  an  angle  of  45°.  Project  the 
revolved  surface  and  find  the  development  when  opened  on  one  of  the  short- 
est edges  of  the  prism. 


DEVELOPMENTS  AND  INTERSECTIONS  59 

PLATE  36 

TRUNCATED  TRIANGULAR    PRISM 


TRUNCATED  HEXAGONAL  PRISM 


m     h 


T 


Revolved 
Surface      2*=- 


PLATE  36 


60  MECHANICAL  DRAWING  PROBLEMS 


TRUNCATED  PENTAGONAL  PRISM 

To  find  the  development  of  a  pentagonal  prism  similar  to  that 
shown,  draw  the  top  view  and  project  the  front  view,  then  draw 
the  revolved  surface.  Lay  out  the  lateral  surface  whose  dimen- 
sions are  found  from  the  top  and  front  views.  Attach  two  plane 
figures  equal  to  the  bottom  and  the  revolved  surfaces. 

Problem  1. — Draw  top  and  front  views  of  the  prism  when  revolved 
counterclockwise  about  its  central  vertical  axis  until  a  face  is  parallel  to  V. 
Show  the  inclined  surface  beginning  at  the  axis  and  making  an  angle  of  30° 
with  the  horizontal.  Project  the  revolved  surface  and  Gnd  the  development 
when  opened  on  its  shortest  edge. 

Problem  2. — Draw  top  and  front  views  of  the  prism  when  revolved  about 
its  central  vertical  axis  through  a  half-revolution.  Let  the  front  view  of 
the  inclined  surface  be  as  shown.  Project  the  revolved  surface  and  find  the 
development  when  opened  on  its  longest  edge. 


TRIANGULAR  PYRAMID 

Since  none  of  the  inclined  edges  of  the  pyramid  are  parallel  to 
either  H  or  V,  it  is  necessary  to  revolve  one  edge  until  it  is  parallel 
to  one  plane.  The  method  shown  is  as  follows:  Revolve  oc  to 
oci,  about  o  as  center,  until  it  is  parallel  to  V.  Project  c\  to  c\, 
and  draw  o'c/,  which  will  be  the  true  length  of  the  edge. 

Problem  1. — Draw  top  and  front  views  of  the  pyramid  when  revolved 
about  its  vertical  axis  through  an  angle  of  180°,  and  find  the  development. 

Problem  2. — Draw  top,  front,  and  side  views  of  a  pyramid  3j  inches  high 
having  a  triangular  base,  the  length  of  each  side  being  2  J  inches.  Let  one  of 
its  lateral  edges  be  parallel  to  P  and  visible  on  V,  and  find  the  development. 

For  additional  figures  see  page  90. 


DEVELOPMENTS  AND  INTERSECTIONS  61 

PLATE  37 


TRUNCATED   PENTAGONAL  PRISM 


TRIANGULAR    PYRAMID 


PLATE  38 


62  MECHANICAL  DRAWING  PROBLEMS 


TRUNCATED    SQUARE   PYRAMID 

To  find  the  true  lengths  of  the  edges  in  this  pyramid,  it  is 
necessary  to  revolve  one  edge  into  a  position  parallel  to  V.  The 
drawing  shows  the  revolved  position  of  one  edge  in  which  the 
true  lengths  are  shown  by  f[  b[,  and  e(b{. 

Problem  1. — Draw  top  and  front  views,  also  the  revolved  surface,  and 
find  the  development  of  the  truncated  prism  when  opened  on  one  of  its 
short  edges. 

Problem  2. — Draw  top,  front,  and  side  views  of  the  truncated  pyramid, 
also  the  revolved  surface,  and  find  the  development  when  the  inclined  surface 
makes  an  angle  of  30°  with  the  horizontal  plane.  Let  the  height  be  2J 
inches  and  let  the  pattern  be  opened  on  one  of  its  shortest  edges. 

For  additional  figures  see  page  91. 


SCALENE  PYRAMID 

Revolve  two  edges  into  positions  parallel  to  V.  Their  true 
lengths  are  then  shown  by  o'b{,  and  o'c{. 

Problem  1. — Draw  the  base  of  the  pyramid  when  turned  through  an 
angle  of  180°  from  the  position  shown,  the  apex  to  remain  as  in  the  drawing. 
Complete  the  top  view,  and  project  the  front  view.  Find  the  development 
when  opened  on  one  of  its  long  edges. 

Problem  2. — Draw  top  and  front  views  of  the  pyramid  as  shown,  and  let 
it  be  truncated  by  a  horizontal  plane  If  inches  from  its  base.  Find  the 
development  when  opened  on  the  long  edge. 


DEVELOPMENTS  AND  INTERSECTIONS  63 
PLATE  39 

TRUNCATED  SQUARE  PYRAMID 


SCALENE  PYRAMID 


PLATE  40 


64  MECHANICAL  DRAWING  PROBLEMS 


TRUNCATED  CYLINDER  AND  CONE 

To  find  the  revolved  surface  of  a  truncated  cylinder  or  a  cone, 
the  top  view  is  divided  into  any  convenient  number  of  equal  parts. 
These  divisions  are  projected  to  the  front  view.  The  revolved 
surface,  which  is  an  ellipse,  may  then  be  found  by  drawing  lines 
at  right  angles  to  the  surface  from  the  points  in  the  front  view, 
and  on  these  laying  off  the  various  widths  as  found  in  the  top 
view.  A  study  of  point  2  in  the  various  views  will  make  the 
method  clear. 

TRUNCATED  CYLINDER 

Problem  1. — Draw  top  and  front  views,  the  revolved  surface,  the  side 
view  of  the  inclined  surface,  and  find  the  development  of  the  truncated 
cylinder  when  opened  on  its  shortest  element.  Let  A  =  2  inches,  B  =  Z\ 
inches,  and  C  =  1  inch. 

Problem  2. — Draw  top  and  front  views,  the  revolved  surface,  the  side 
view  of  the  inclined  surface,  and  find  the  development  of  the  truncated 
cylinder  when  opened  on  its  longest  element.  Let  A  =  If  inches,  B  —  3J 
inches,  and  let  the  inclined  surface  make  an  angle  of  60°  with  the  horizontal 
plane. 


TRUNCATED  CONE 

The  true  lengths  of  the  elements  of  the  cone  may  be  found  by 
revolving  them  about  the  axis  into  positions  parallel  to  V. 

Problem  1. — Draw  top,  front,  and  side  views,  the  revolved  surface,  and 
find  the  development  of  the  truncated  cone  when  opened  on  its  shortest 
element.  Let  A  =  2%  inches,  .6=4  inches,  C  —  1  inch,  and  B  =  45°. 

Problem  2. — Draw  top,  front,  and  side  views,  the  revolved  surface,  and 
find  the  development  of  the  truncated  cone  when  opened  on  its  longest 
element.  Let  A  =  2|  inches,  5=4  inches,  C  =  1  inch,  and  0  =  60°. 


DEVELOPMENTS  AND  INTERSECTIONS  65 
PLATE  41 

TRUNCATED    CYLINDER 


Top  View  Revolved   Surface 


Front  View 


Top  vie*  TRUNCATED   CONE 


Front   View 


Pattern 


PLATE  42 


66  MECHANICAL  DRAWING  PROBLEMS 

CONIC  SECTIONS 
(First  and  Second  Drawings) 

The  intersection  formed  by  a  cone  and  a  plane,  making  the 
same  angle  with  the  axis  as  the  elements,  is  a  parabola. 

The  intersection  formed  by  a  cone  and  a  plane,  making  a 
smaller  angle  with  the  axis  than  the  elements,  is  an  hyperbola. 

The  curves  shown  in  the  first  drawing  are  found  by  the  method 
of  intersecting  elements.  The  curves  shown  in  the  second  draw- 
ing are  found  by  the  method  of  cutting  planes. 

Draw  two  views  showing  a  cone  cut  by  a  plane.  Draw  V  and 
H  projections  of  an  element  intersected  by  a  plane  giving  c'  and 
c  as  shown  in  the  first  drawing;  or,  draw  V  and  H  projections  of 
a  horizontal  cutting  plane  giving  c'  and  c  as  shown  in  the  second 
drawing.  The  point  formed  by  either  of  these  methods  will  be 
one  point  on  the  required  curve.  The  location  of  the  point  in 
the  revolved  view,  which  will  give  the  true  shape  of  the  curve,  is 
found  by  measurement  from  the  top  or  the  end  views.  Other 
points  are  found  similarly. 

To  find  the  development,  draw  a  sector  the  length  of  whose 
arc  equals  the  circumference  of  the  base  of  the  cone,  and  draw 
elements  the  location  of  which  are  found  from  the  top  view,  as  in 
the  first  drawing;  or,  draw  circular  arcs  the  location  of  which  are 
found  from  the  front  view,  as  in  the  second  drawing.  Locate 
points  found  from  the  front  view  on  elements  or  on  circular  arcs 
and  draw  the  curve. 

CONIC  SECTION 
(First  Drawing) 

Problem  1. — Complete  the  views  shown  by  the  intersecting  element 
method.  Let  A  =  3,  B  =  3£,  and  C  =  If  inches. 

Problem  2. — Complete  the  views  shown  by  the  horizontal  cutting  plane 
method.  Assume  dimensions  for  the  cone  and  a  suitable  location  for  the 
plane. 

For  figures  of  pyramids  see  pages  90  and  91. 

CONIC  SECTION 
(Second  Drawing) 

Problem  1. — Complete  the  views  shown  by  the  horizontal  cutting  plane 
method.  Let  A  =  3,  B  =  3J,  C  =  H  inches,  and  6  =  80°. 

Problem  2. — Complete  the  views  shown  by  the  intersecting  element 
method.  Assume  dimensions  for  the  cone  and  a  suitable  location  and 
angle  for  the  plane. 

For  figures  of  pyramids  see  pages  90  and    91. 


DEVELOPMENTS  AND  INTERSECTIONS  67 

PLATE  43 


CONIC   SECTION 

FIRST   DRAWING 


Pat  fern 


Front  View 


Side    View 


CONIC  SECTION 

SECOND   DRAWING 


Pattern 


Top  View 


Front  View 


Side  View 
PLATE  44 


68  MECHANICAL  DRAWING  PROBLEMS 


INTERSECTION 

The  curve  formed  by  the  intersection  of  two  objects  is  called 
the  line  of  intersection. 

This  line  may  be  found  by  the  intersecting  elements  method, 
or  by  the  use  of  cutting  planes.  See  pages  20  and  21. 

INTERSECTING  CYLINDERS 

The  top  view  of  an  element  passing  through  point  2i  in  the 
drawing,  will  penetrate  the  vertical  cylinder  at  2.  This  point  of 
penetration  projected  to  the  front  view  of  the  element  will  give 
2',  a  point  on  the  line  of  intersection.  Other  points  are  located 
similarly. 

Problem  1. — Find  the  line  of  intersection  of  the  first  figure  when  A  =  2\, 
B  =  3$,  C  =  11,  D  =  2,  and  E  =  1J  inches. 

Find  the  line  of  intersection  of  the  second  figure  when  A  =  3,  B  =  3J, 
C  =  If,  D  =  2J,  and  E  =  1|  inches. 

Problem  2. — Find  the  line  of  intersection  of  the  first  figure  when  A  =  3, 
B  =  3f,  C  =  If,  D  =  3i,  and  E  =  \  inches.  Let  the  length  of  the  hori- 
zontal cylinder  be  4  inches. 

Find  the  line  of  intersection  of  the  second  figure  when  A  =  2$,  B  =  3%,  C 
=  If,  D  =  2%,  and  E  =  f  inches.  Let  the  length  of  the  horizontal  cylinder 
be  3f  inches. 

For  additional  figure  see  A,  page  92. 

INTERSECTING  SOLIDS 

Points  on  the  line  of  intersection  in  the  front  views  are  found 
by  assuming  the  location  of  the  top  view  of  an  element  and  find- 
ing its  front  view.  The  point  of  penetration  projected  from 
the  top  view  to  the  front  view  will  give  one  point  on  the  line  of 
intersection. 

Problem  1. — Find  the  line  of  intersection  of  the  first  figure  when  A  =  3, 
B  =  3|,  C  =  If,  D  =  2$,  and  E  =  1|  inches. 

Find  the  line  of  intersection  of  the  second  figure  when  A  =  3,  B  =  85, 
C  =  If,  D  =  2%,  and  E  =  1|  inches. 

Problem  2. — Find  the  line  of  intersection  of  the  left-hand  figure  when 
A  =  2J,  B  =  3i  C  =  If,  D  =  2f ,  and  E  =  \  inches.  Let  the  length  of 
the  horizontal  cylinder  be  3 £  inches. 

Find  the  line  of  intersection  of  the  right-hand  figure  when  A  =  2\, 
B  =  3i,  C  =  If,  D  =  2%,  and  E  =  f  inches.  Let  the  length  of  the  hori- 
zontal prism  be  4  inches. 


DEVELOPMENTS  AND  INTERSECTIONS  69 
PLATE  46 

INTERSECTING  CYLINDERS 


INTERSECTING  SOLIDS 


PLATE  46 


70  MECHANICAL  DRAWING  PROBLEMS 


CONE  AND  CYLINDER 

The  intersection  of  the  cone  and  cylinder  is  found  by  dividing 
the  base  of  the  cone  into  any  number  of  equal  parts.  From  these 
divisions  draw  the  front  and  the  side  views  of  elements  of  the 
cone.  Project  from  the  point  where  the  elements  penetrate  the 
cylinder,  shown  in  the  side  view,  to  the  corresponding  front  view 
projections  of  these  elements.  A  study  of  point  2  will  make  the 
method  clear. 

Problem  1. — Find  the  intersection  when  A  =  4|,  B  =  5,  C  =  2%,  D  = 
5 £,  and  E  =  If  inches. 

Problem  2.— Find  the  intersection  when  A  =  4,  B  =  5,  C=2J,  D  = 
5 1,  and  E  =  If  inches. 

For  additional  figures  see  C,  page  92;  also,  A  and  B,  page  95. 


CONE  AND  PRISM 

The  intersection  of  the  cone  and  prism  is  found  by  assuming 
a  point  as  4"  on  the  end  of  the  prism.  Through  this  point  draw 
the  side  view  of  an  element  of  the  cone.  Find  the  front  view  of 
this  element.  Project  from  the  point  where  the  element  pene- 
trates the  prism  in  the  side  view,  to  the  front  view,  giving 
4',  a  point  on  the  line  of  intersection.  Other  points  are  found 
similarly. 

Problem  1. — Find  the  line  of  intersection  when  A  =  4,  B  =  5,  C  =  2, 
D  =  5%,  and  E  =  2  inches. 

Problem  2. — Find  the  line  of  intersection  when  A  =4,  B  =  5,  C  =  if , 
D  =  5,  and  E  =  1 1  inches. 


DEVELOPMENTS  AND  INTERSECTIONS  71 

PLATE  47 


CONE  AND  CYLINDER 


Side  View 


Front  View 


CONE  AND  PRISM 


Side  View 


PLATE  48 


72  MECHANICAL  DRAWING  PROBLEMS 


THREE-PIECE  ELBOW 

To  find  the  development  of  a  three-piece  elbow,  first  draw  the 
front  view  and  project  the  top  view.  Then  divide  the  surface 
into  any  number  of  equal  parts,  and  draw  elements.  Lay  out  a 
surface  whose  length  equals  the  circumference  of  the  pipe.  Di- 
vide this  length  into  the  same  number  of  parts  as  the  pipe.  On 
vertical  lines  drawn  through  the  divisions  lay  off  distances  equal 
to  the  lengths  of  the  elements  obtained  from  the  front  view,  and 
draw  the  curves. 

The  ellipse  in  the  top  view  is  the  line  of  intersection  of  the 
horizontal  and  oblique  members  of  the  elbow.  It  is  found  by 
projection  from  the  front  view. 

Problem  1. — Draw  front  and  top  views,  and  find  the  development  for  a 
three-piece  pipe  when  A  =  2,  B  =  3,  C  =  1\,  D  =  U,  and  E  =  1  inches. 

Problem  2. — Draw  front  and  top  views,  and  find  the  development  for  a 
three-piece  pipe  when  A  =  1\  inches.  Assume  suitable  dimensions  for  B, 
C,  D,  and  E. 

For  additional  figures  see  A,  and  B,  page  93. 

VERTICAL  AND  OBLIQUE  CYLINDERS 

To  find  the  intersection  of  a  vertical  and  an  oblique  cylinder 
similar  to  those  shown,  first  draw  the  outline  of  the  front  view  and 
project  the  top  view.  Divide  the  oblique  cylinder,  or  pipe,  into 
any  number  of  equal  parts,  and  draw  elements  in  both  views.  One 
point  for  the  line  of  intersection  is  found  by  projecting  from  the 
point  where  an  element  pierces  the  vertical  pipe,  shown  in  the  top 
view,  to  its  front  view.  A  study  of  point  1,  in  the  drawing,  will 
make  the  method  clear. 

To  develop  the  half-pattern  for  the  oblique  pipe,  lay  off  a  sur- 
face whose  width  equals  the  semi-circumference,  and  whose 
length  equals  the  length  of  the  pipe.  Divide  this  surface  into  the 
required  number  of  parts.  On  these  parts  lay  off  from  mn  dis- 
tances obtained  by  measurement  from  the  front  view. 

Problem  1. — Draw  front  and  top  views,  and  find  the  development  for  the 
pipes  as  shown.  Let  A  =  2|,  B  =  4£,  and  C  =  1§  inches. 

Problem  2. — Draw  front  and  top  views,  and  find  the  development  for 
two  pipes  similar  to  those  shown.  Let  A  =  2,  B  =  4£,  and  C  =  1|  inches. 

For  additional  figures  see   B  and  D,  page  92. 


DEVELOPMENTS  AND  INTERSECTIONS  73 

PLATE  49 


THREE-PIECE    ELBOW 


1  ! ! 

\9    I       ' 


VERTICAL  AND  OBLIQUE  CYLINDERS 

Half 
Pattern 

^ 


PLATE  50 


74  MECHANICAL  DRAWING  PROBLEMS 


OFFSET  PIPES  AND  ELBOWS 

Offset  pipes  and  elbows  may  be  made  from  straight  or  tapering 
pipes  by  cutting  at  suitable  angles  as  shown  in  the  drawings. 

To  niake  an  offset  pipe,  select  two  points  on  the  axis  of  the  pipe, 
thus  dividing  it  into  three  parts.  Lay  out  these  parts  of  the 
axis  to  give  the  amount  of  offset  wanted.  Measure  the  angle  the 
inclined  axis  makes  with  the  original  axis.  This  angle  divided  by 
two  will  give  the  angle  of  cut. 

The  angle  of  cut  for  a  three-piece  elbow  will  be  one-half  the 
angle  the  oblique  section  makes  with  the  uncut  pipe. 

CIRCULAR   OFFSET  PIPE 

Problem  1. — Draw  an  offset  pipe,  and  find  the  development  when  A  = 
If,  B  =  11,  C  =  4,  D  =  1J,  and  E  =  21  inches. 

Problem  2. — Draw  an  offset  pipe,  and  find  the  development  when  A  = 
If  and  C  =  4  inches.  Let  6  =  45°.  Assume  the  other  dimensions. 

For  additional  figures  see  A,  B,  aid  C,  page  93. 


THREE-PIECE    CONICAL   ELBOW 

Problem  1. — Draw  a  three-piece  right-angled  conical  elbow,  and  find  the 
development  when  A  =  2f,  B  =  1J,  C  =  2J,  D  =  3,  and  E  =  1J  inches. 

Problem  2. — Draw  a  conical  offset  pipe,  and  find  the  development  when 
A  =  1\  and  B  =  U  inches.  Let  6  =  60°.  Assume  the  other  dimensions 
and  the  amount  of  offset. 

For  additional  figures  see  D,  E,  and  F,  page  93. 


DEVELOPMENTS  AND  INTERSECTIONS  75 

PLATE  51 


CIRCULAR    OFF-SET  PIPE 


THREE-PIECE   CONICAL    ELBOW 


PLATE  "52 


76  MECHANICAL  DRAWING  PROBLEMS 


INTERSECTING  PIPES 

The  intersection  of  two  pipes  of  equal  diameters  with  inter- 
secting axes,  oblique  or  at  right  angles  to  each  other,  is  shown  by 
straight  lines  in  the  front  view. 

The  intersection  of  two  pipes  of  unequal  diameters  with  axes 
intersecting  or  offset,  oblique  or  at  right  angles,  is  shown  by 
curved  lines  in  the  front  view. 

The  ellipses  in  the  top  views  of  the  oblique  pipes  may  be  found 
by  projection,  as  in  previous  problems,  or  may  be  drawn  after 
the  lengths  of  the  axes  have  been  determined,  as  explained  for 
Figs.  31  or  32. 

A  study  of  the  reference  letters  and  figures  in  the  drawings 
should  enable  the  student  to  work  the  following  problems : 

INTERSECTING  PIPES 
(Same  Diameters) 

Problem  1. — Find  the  development  for  two  intersecting  pipes  of  equal 
diameters  and  intersecting  axes.  Let  6  =  45°,  A  =  2J,  B  =  4,  C  =  \, 
and  D  =  3  inches. 

Problem  2. — Find  the  development  for  two  intersecting  pipes  of  equal 
diameters  and  intersecting  axes.  Let  0  =  60°  and  A  =  2  inches.  Assume 
other  suitable  dimensions. 

For  additional  figures  see  A  and  B,  page  92. 


INTERSECTING  PIPES 
(Different  Diameters) 

Problem  1. — Find  the  development  for  two  intersecting  pipes  of  unequal 
diameters  and  non -intersecting  axes.  Let  6  =  45°,  A  =  2%,  B  =  4,  C  = 
If,  D  =  4f,  E  =  f,  and  F  =  |  inches. 

Problem  2. — Find  the  development  for  two  intersecting  pipes  of  unequal 
diameters  and  non-intersecting  axes.  Let  6  =  45°,  A  =  2j,  C  =  1J, 
and  F  =  |  inches.  Assume  other  suitable  dimensions. 

For  additional  figures  see  C  and  D,  page  92. 


DEVELOPMENTS  AND  INTERSECTIONS  77 

PLATE  63 


INTERSECTING 
PIPES 

Same   Diam's 


INTERSECTING    PIPES 

Different   Diam's 


PLATE  54 


78  MECHANICAL  DRAWING  PROBLEMS 


TRANSITION  PIECE 
Octagonal   Outlet 

To  find  the  development  of  transition  piece  similar  to  that 
shown,  draw  top  and  front  views.  Find  true  dimensions  of  the 
surfaces,  of  which  there  are  two  kinds,  and  lay  out  the  pattern 
as  shown. 

The  surface  adeb  in  the  development  is  shown  in  its  true  height 
by  fib'  in  the  front  view,  while  the  lengths  de  and  ab  are  found 
from  the  top  view. 

Problem  1. — Draw  a  transition  piece  having  a  square  inlet  and  an  oc- 
tagonal outlet,  and  find  the  development  when  A  =  2J  and  B  =  3  inches. 
Let  the  outlet  be  as  shown. 

Problem  2. — Draw  a  transition  piece  having  a  square  inlet  and  a  If-inch 
square  outlet  and  find  the  development  when  A  =  2f  and  B  =  2>\  inches. 


TRANSITION  PIECE 
Round  Outlet 

To  find  the  development  of  a  transition  piece  similar  to  that 
shown,  draw  top  and  front  views.  Divide  ed  into  four  equal 
parts  and  project  to  the  front  view.  Construct  a  true  lengths 
diagram,  as  follows:  On  a  horizontal  line  lay  off  lengths  be,  61, 
and  62  and  erect  vertical  lines  of  lengths  equal  to  the  height  of 
the  object.  The  true  lengths  are  then  drawn  as  shown.  Draw 
the  triangle  abe.  From  e  draw  an  arc  of  radius  el,  found  in  the 
top  view,  and  from  6  draw  an  intersecting  arc  of  radius  61 1,  found 
from  the  diagram.  The  intersection  of  these  arcs  will  be  one 
point  on  the  required  curve.  Other  points  are  found  similarly. 
This  is  called  the  triangulation  method  of  development. 

Problem  1. — Find  the  development  for  a  transition  piece  having  a  square 
inlet  and  a  round  outlet  when  A  =  2|,  B  =  3,  and  C  =  If  inches. 

Problem  2. — Find  the  development  for  a  transition  piece  having  a  square 
inlet  and  a  round  outlet  when  A  =  2$,  B  =  3,  and  C  =  3  inches. 


DEVELOPMENTS  AND  INTERSECTIONS  79 

PLATE  55 


TRANSITION  PIECE 

OCTAGONAL    OUTLET 


TRANSITION  PIECE 

ROUND    OUTLET 


PLATE  56 


80  MECHANICAL  DRAWING  PROBLEMS 


SCALENE  CONE 

To  find  the  development  of  a  scalene  cone,  draw  front  and  top 
views.  Divide  the  base  into  any  number  of  equal  parts.  Lay 
out  a  true  lengths  diagram  and  find  the  development  by  the  inter- 
secting arc  method.  A  study  of  the  drawing  will  make  the  solu- 
tion clear. 

Problem  1. — Find  the  development  for  a  scalene  cone  with  a  circular 
base  when  A  =  3,  B  =  3i,  and  C  =  2f  inches. 

Problem  2. — Find  the  development  for  the  frustum  of  a  scalene  cone 
when  A  =  2f,  B  =  3£,  C  =  3,  and  D  =  If  inches. 


TRANSITION  PIECE 

To  find  the  development  of  the  transition  piece  shown,  draw 
top  and  front  views.  Divide  one  half  of  the  top  view  into  an 
even  number  of  parts,  project  to  the  front  view,  and  draw  ele- 
ments and  diagonals  as  shown.  Lay  out  the  element  and  the 
diagonal  diagrams  by  laying  off  on  horizontal  lines  the  lengths 
measured  from  the  top  view,  as  bases  of  right-angled  triangles, 
whose  heights  equal  the  height  of  the  object.  The  true  lengths 
of  the  elements  and  the  diagonals  will  be  equal  to  the  hypothe- 
nuses  of  these  triangles. 

Find  the  development  by  beginning  at  b,  an  assumed  point, 
and  locating  points  10,  9,  8,  etc.,  by  the  intersecting  arc  method. 
To  locate  point  10,  for  instance,  draw  an  arc  from  6  as  center  and 
of  radius  610,  found  from  the  top  view;  also,  draw  an  intersecting 
arc  from  d  as  center  and  of  radius  olO,  found  from  the  diagram 
of  diagonals.  The  intersection  of  the  arcs  will  give  point  10. 
Other  points  are  found  similarly. 

Problem  1. — Find  the  development  for  the  transition  piece  when  A  =  4, 
B  =  3,  C  =  2\,  D  =  If,  and  E  =  2  inches. 

Problem  2. — Find  the  development  for  the  transition  piece  when  A  =  4, 
B  =  3J,  C  =  2|,  D  =  2,  and  E  =  If  inches. 


DEVELOPMENTS  AND  INTERSECTIONS  81 

PLATE  57 


SCALENE  CONE 


///         !  t 

m/aii. 

I'      &•          3'          4-'       S'6  C' 


TRANSITION  PIECE- 


2'          4-'  6'  &          10 


a  +  aeeiob    4-2606/0 


PLATE  68 


82  MECHANICAL  DRAWING  PROBLEMS 


INTERSECTION  OF  TWO  PRISMS 

To  find  the  projections  of  two  intersecting  prisms  as  shown, 
proceed  in  the  following  order:  Draw  top  and  front  views  of  B; 
the  axis  of  A;  the  auxiliary  view  of  B,  on  axis  at  right  angles  to 
axis  for  A;  the  auxiliary  view  of  A;  the  front  and  the  top  views 
of  A.  Letter  the  ends  of  the  edges  as  shown. 

To  find  one  point  on  the  intersection,  proceed  as  follows: 
Select  a  point,  as  1,  in  the  top  view.  This  point  will  be  h  in 
the  auxiliary  view.  The  intersection  of  projections  from  land 
li  will  give  I',  a  point  on  the  intersection.  Projections  from  2 
and  2i  on  edge  a,  will  give  2',  another  point  on  the  intersection. 
A  straight  line  drawn  from  1'  to  2'  will  be  a  portion  of  the  inter- 
section. Then  find  3'  and  join  it  to  2'  by  a  straight  line.  Next 
find  4'  and  continue  this  operation  until  the  complete  line  of 
intersection  is  found. 

Problem  1. — Find  the  line  of  intersection  of  the  two  prisms  as  shown. 
Ascertain  the  dimensions  and  angles  by  measuring  the  drawing.  The 
scale  of  the  drawing  is  f  inch  equals  1  inch. 

Problem  2. — Find  the  line  of  intersection  of  the  two  prisms  when  «  = 
10°,  6  =  20°,  and  <£  =  30°.  Ascertain  the  dimensions  of  the  prisms  and 
location  of  the  oblique  axis  by  measuring  the  drawing.  The  scale  of  the 
drawing  is  f  inch  equals  1  inch. 

For  additional  figures  see  page  94. 

DEVELOPMENT  OF  TWO  INTERSECTING  PRISMS 

Find  the  development  of  prism  A,  in  the  upper  drawing,  by 
laying  out  a  surface  equal  to  the  surface  of  the  prism.  Letter 
the  surface  corresponding  to  the  edges.  Point  1,  on  edge  i,  is 
found  by  measuring  its  distance  from  i  in  the  front  view  and 
laying  this  off  from  i  in  the  development.  Point  2  is  found  by 
measuring  the  distance  of  2i  from  i\  in  the  auxiliary  view,  and 
the  distance  from  line  j'h'  in  the  front  view,  and  laying  off  these 
distances  in  the  development.  Other  points  are  found  similarly. 

The  development  for  prism  B  is  found  by  a  similar  method. 

Problem  1. — Find  the  development  of  the  prisms  for  Problem  1  in  the 
INTERSECTION  OF  Two  PRISMS. 

Problem  2. — Find  the  development  of  the  prisms  for  Problem  2  in  the 
INTERSECTION  OF  Two  PRISMS. 


Top  View 


DEVELOPMENTS  AND  INTERSECTIONS  83 

PLATE  59 


INTERSECTION  or  Two  PRISMS 

v,\  a. 


Auxiliary    View 


Front    View 


DEVELOPMENT   OF 
Two  INTERSECTING    PRISMS      e 


f     e 


PLATE  60 


84  MECHANICAL  DRAWING  PROBLEMS 

INTERSECTION  OF  TWO  CONES 
First  Method 

Cutting  Plane  Method. — The  intersection  of  two  cones  may  be 
found  by  means  of  a  number  of  cutting  planes,  each  containing 
elements  of  both  surfaces.  The  intersection  of  elements  in  the 
same  plane  will  give  points  on  the  line  of  intersection. 

Draw  a  line  of  indefinite  length  through  the  apexes  a  and  e. 
Draw  lines  through  the  bases,  locating  points  k,  x,  and  y.  From  k, 
draw  lines  at  right  angles  to  the  bases.  From  d  and  h,  as  centers, 
draw  half-circles  as  shown.  " 

Select  any  point,  as  q,  on  the  revolved  view  of  the  base  of  the 
smaller  cone,  and  draw  a  line  from  x  through  q,  giving  points  p 
and  n.  With  k  as  center,  draw  an  arc  from  n  to  n'  and  a  line  from 
n'  to  y,  giving  points  r  and  s  on  the  revolved  view  of  the  base  of 
the  larger  cone. 

The  lines  drawn  from  x  and  y  to  n  and  n'  are  the  traces  of  a 
plane  passing  through  the  apexes  of  the  cones  and  will  cut  ele- 
ments from  both  cones.  The  intersections  of  these  elements  will 
locate  four  points  on  the  line  of  intersection.  Two  of  these  are 
shown  by  points  1  and  2.  Other  points  on  the  intersection  may 
be  found  by  drawing  additional  planes  from  o,  m,  and  /. 

A  study  of  the  drawing  should  enable  the  student  to  find  the 
intersection  in  the  end  view. 

Problem  1. — Find  the  line  of  intersection  in  the  front  and  the  side  views 
of  the  cones  as  shown.  For  dimensions,  measure  the  drawing  to  a  scale  of 
f  inch  equals  1  inch. 

Problem  2. — Find  the  line  of  intersection  in  the  front  and  the  side  views 
of  two  cones,  similar  to  those  shown,  the  axes  intersecting  and  at  right 
angles  to  each  other.  For  dimensions,  measure  the  drawing  to  a  scale  of 
f  inch  equals  1  inch. 

For  additional  figures  see  C,  D,  E,  and  F,  page  95. 

DEVELOPMENT  OF  TWO  INTERSECTING  CONES 

Draw  sectors  equal  to  the  convex  surfaces  of  cones  A  and  B. 
Lay  off  points  r,  s,  and  p,  obtained  from  the  bases  of  the  front 
view,  and  draw  the  elements.  On  these  elements  locate  points  1 
and  2,  their  true  distance  from  r,  s,  and  p  being  found  from  the 
front  view.  Additional  points  are  found  similarly. 

Problem  1. — Find  the  developments  for  Problem  1,  INTERSECTION  OP 
Two  CONES,  First  Method. 

Problem  2. — Find  the  developments  for  Problem  2,  INTERSECTION  OP 
Two  CONES,  First  Method. 


DEVELOPMENTS  AND  INTERSECTIONS  85 

PLATE  61 


INTERSECTION    OF-  Two    CONES 

First    Method 


Side   View 


.  DEVELOPMENT   or 
Two  INTERSECTING  CONES 


Pattern    for  A 


Pattern    for  B 


PLATE   62 


MECHANICAL  DRAWING  PROBLEMS 

INTERSECTION  OF  TWO  CONES 
Second  Method 

Concentric  Sphere  Method. — The  projections  of  concentric 
spheres,  drawn  with  the  intersection  of  the  axes  of  two  cones  as  a 
center,  will  cut  circles  from  both  surfaces,  where  the  spheres 
and  cones  intersect.  The  intersections  of  these  circles  will  give 
points  on  the  line  of  intersection. 

With  o  as  center,  draw  the  projection  of  a  sphere  of  an  assumed 
radius  op,  cutting  cone  A  at  r  and  t,  and  cone  B  at  q  and  s.  Lines 
drawn  from  these  points,  at  right  angles  to  the  axes  of  the  cones, 
show  the  vertical  projections  of  four  circles,  two  of  which  are 
parallel  to  the  base  of  A,  and  two  parallel  to  the  base  of  B.  The 
intersections  of  these  circles  give  points  1,  2,  and  3  on  the  line  of 
intersection.  Point  4  is  found  by  drawing  a  portion  of  a  sphere 
of  an  assumed  radius  oy. 

A  study  of  the  drawing  should  enable  the  student  to  find  addi- 
tional points  in  the  front  view,  also  the  points  in  the  top  and  the 
side  views. 

Problem  1. — Find  the  line  of  intersection  of  the  cones  as  shown.  For 
dimensions,  measure  the  drawing  to  a  scale  of  f  inch  equals  1  inch. 

Problem  2. — Find  the  line  of  intersection  in  three  views  of  the  two  cones 
when  the  axes  are  at  right  angles  to  each  other.  For  dimensions,  measure 
the  drawing  to  a  scale  of  f  inch  equals  1  inch. 

For  additional  figures  see  C,  D,  E,  and  F,  page  95. 

DEVELOPMENT    OF    TWO    INTERSECTING    CONES 

Draw  a  sector  equal  to  the  convex  surface  of  cone  B.  Draw 
the  elements  finding  their  location  from  the  revolved  view  of  the 
base  of  the  cone  as  shown  in  the  front  view.  Circular  arcs  with 
radii  measured  on  kf  in  the  front  view,  and  drawn  in  the  pattern, 
will  intersect  the  elements  giving  points  on  the  required  curve 
as  shown. 

To  locate  the  elements  for  pattern  A,  it  will  be  necessary  to 
draw  a  revolved  view  of  the  base,  similar  to  that  for  B,  to  find 
the  location  of  elements  drawn  through  the  points  on  the  line  of 
intersection. 

Problem  1. — Find  the  developments  for  Problem  1,  INTERSECTION  OF 
Two  CONES,  Second  Method. 

Problem  2. — Find  the  developments  for  Problem  2,  INTERSECTION  OF 
Two  CONES,  Second  Method. 


DEVELOPMENTS  AND  INTERSECTIONS  87 

PLATE  63 


Top  View 


INTERSECTION  or  Two  CONES 

Second    Method 


Front    View 


Side  View 


DEVELOPMENT  or  Two  INTERSECTING    CONES 


Pattern    for  A 


Pattern     for    B 


PLATE  64 


88  MECHANICAL  DRAWING  PROBLEMS 

INTERSECTION   OF   TWO   CONES 
Third  Method 

Revolved  Section  Method. — Points  on  the  intersection  of  two 
cones  may  be  found  by  the  intersection  of  lines  shown  by  a 
number  of  revolved  sections. 

A  revolved  section,  produced  by  a  plane  cutting  a  triangle  from 
the  one  and  a  curved  line  from  the  other  of  two  intersecting  cones, 
will  show  two,  or  four,  points  on  the  line  of  intersection. 

Divide  the  revolved  view  of  gh  into  eight  equal  parts  and  pro- 
ject these  points  of  division  to  gh,  giving  points  p,  I,  and  n. 
From/  draw  plane  traces  through  p,  I,  and  n,  giving  points  r,  s,  and 
t.  Divide  the  bottom  view  of  cone  A  into  equal  parts  and  draw 
elements  as  shown.  From  the  intersections  of  fs  and  the  ele- 
ments cut,  also  from  I,  draw  lines  at  right  angles  to/s.  Draw/Y 
parallel  to  fs.  On  fs'  as  an  axis,  find  the  revolved  section  cut 
from  A  by  the  plane  fs.  From/',  through  k"l" ',  equal  to  k'lf,  draw 
lines  intersecting  the  revolved  section  of  A  at  points  2-2.  These 
points  projected  back  to/s  will  be  two  points  on  the  line  of  inter- 
section. Additional  points  are  found  from  the  revolved  sections 
C  and  E. 

Problem  1. — Find  the  line  of  intersection  of  the  cones  as  shown.  For 
dimensions,  measure  the  drawing  to  a  scale  of  |  inch  equals  1  inch.  Let  the 
axes  make  an  angle  of  30°  with  each  other. 

Problem  2. — Find  the  line  of  intersection  of  two  cones,  similar  to  those 
shown,  whose  axes  make  an  angle  of  45°  with  each  other.  For  dimensions, 
measure  the  drawing  to  a  scale  of  f  inch  equals  1  inch. 

For  additional  figures  see  C,  D,  E,  and  F,  page  95. 

DEVELOPMENT  OF  TWO  INTERSECTING  CONES 

Draw  the  front  view  showing  the  line  of  intersection,  and  the 
elements  v,  w,  and  x.  These  elements  are  found  by  drawing  lines 
through  the  points  found  on  the  line  of  intersection  in  the  upper 
drawing. 

A  study  of  the  drawings  should  enable  the  student  to  complete 
the  developments. 

Problem  1. — Find  the  developments  for  Problem  1,  INTERSECTION  OF 
Two  CONES,  Third  Method. 

Problem  2. — Find  the  developments  for  Problem  2,  INTERSECTION  OF 
Two  CONES,  Third  Method. 


DEVELOPMENTS  AND  INTERSECTIONS  89 

PLATE  65 


x  \JNTERSECTION  OF  Two  CONES 

2-$      Third    Method 


Side  View 


C-O-E 

Revolved   Sections    i 


DEVELOPMENT  OF  Two    INTERSECTING    CONES 


Pattern     for  A 


Pattern     for   B 


PLATE  66 


90 


MECHANICAL  DRAWING  PROBLEMS 


TRIANGULAR    PYRAMID 

d 


c  Front  View  °' 


Front  View 


PENTAGONAL    PYRAMID 


a1  a; 

Supplementary  problems. 


DEVELOPMENTS"AND  INTERSECTIONS 


SQUARE    PYRAMID 

e 


a'   a', 

HEXAGONAL   PYRAMID 


Supplementary  problems 


92 


MECHANICAL  DRAWING  PROBLEMS 


Supplementary  problems. 


DEVELOPMENTS  AND  INTERSECTIONS  93 


Supplementary  problems. 


94 


MECHANICAL  DRAWING  PROBLEMS 


Suj  plementary  problems. 


DEVELOPMENTS  AND  INTERSECTIONS  95 


Supplementary  problems. 


96  MECHANICAL  DRAWING  PROBLEMS 

SECTION  III 
ISOMETRIC  AND  OBLIQUE  DRAWING 

ISOMETRIC   DRAWING 

Isometric  drawing  is  a  branch  of  mechanical  drawing  which 
shows  three  faces  of  an  object  in  one  view,  and  is  based  on  the 
following  Principles: 

1.  Three  axes  are  drawn  from  a  common  point,  called  the 
origin,  on  a  horizontal  line;  one  is  drawn  vertical,  one  30°  to  the 
left,  and  one  30°  to  the  right. 

2.  The  axes  represent  lines  which  are  mutually  perpendicular 
to  each  other,  and  on  them  length,  width,  and  height  may  be 
measured. 

3.  Measurements  of  length,  width,  and  height  can  be  made  only 
on  the  axes,  or  on  lines  parallel  to  the  axes. 

4.  Lines  which  are  parallel  in  an  object  are  parallel  in  the 
drawing. 

5.  Lines  which  are  vertical  in  an  object  are  vertical  in  the 
drawing,  and  will  be  drawn  in  their  true  lengths. 

6.  Lines  which  are  not  parallel  to  one  of  the  isometric  axes  are 
said  to  be  non-isometric,  and  cannot  be  measured  in  their  true 
lengths. 

7.  Non-isometric  lines  are  located  by  offsets,  and  may  be  either 
longer  or  shorter  than  their  true  measurements. 

8.  Lines  which  are  at  right  angles  in  an  object  are  shown  at  60° 
or  120°  to  each  other  in  the  drawing. 

9.  Isometric  angles  cannot  be  measured  in  degrees. 

10.  An  isometric  circle  is  an  ellipse,  and  a  quarter-circle  will  be 
shown  in  an  angle  of  either  60°  or  120°. 

ISOMETRIC  BLOCKS 

Problem  1. — Make  a  drawing  of  the  figures  shown  beginning  with  a  at 
the  origin  of  the  axes. 

Problem  2. — Make  a  drawing  of  the  figures  shown  beginning  with  b  at 
the  origin  of  the  axes. 

JOINTS 

Problem  1. — Make  a  drawing  showing  the  joints  beginning  with  a  at 
the  origin  of  the  axes. 

Problem  2. — Make  a  drawing  showing  the  joints  beginning  with  b  at  the 
origin  of  the  axes. 


ISOMETRIC  DRAWING 


97 
PLATE  67 


ISOMETRIC  BLOCKS 


Isometric  Axes 


MORTISE  AND  TENON 


JO/NTS 


'    ^> 


HALVED   TEE 


PLATE  68 


98  MECHANICAL  DRAWING  PROBLEMS 


JOINTS 

This  drawing  shows  two  joints  in  which  the  vertical  member 
of  the  left-hand  figure  is  withdrawn  vertically  through  a  distance 
of  |  inch,  while  the  vertical  member  of  the  right-hand  figure  is 
withdrawn  horizontally  through  a  distance  of  1|  inches. 

Problem  1. — Make  a  drawing  of  the  figures  shown  beginning  with  the 
corners  a  at  the  origin  of  the  axes. 

Problem  2. — Make  a  drawing  of  the  figures  shown  beginning  with  the 
corners  6  at  the  origin  of  the  axes. 


MORTISE  AND  TENON  JOINTS 

This  drawing  shows  two  mortise  and  tenon  joints  in  which  the 
horizontal  member  of  the  left-hand  figure  is  withdrawn  1  inch, 
while  the  vertical  member  of  the  right-hand  figure  is  withdrawn 
1^  inches. 

Problem  1. — Make  a  drawing  showing  the  joints  beginning  with  the 
corners  a  at  the  origin  of  the  axes. 

Problem  2. — Make  a  drawing  showing  the  joints  beginning  with  the 
corners  b  at  the  origin  of  the  axes. 


ISOMETRIC  DRAWING 


99 
PLATE  69 


JO/ NTS 


HALVED  DOVETAIL 


MORTISE  AND  TENON 


MORTISE  AND  TENON  JOINTS 


PLATE  70 


100  MECHANICAL  DRAWING  PROBLEMS 


MITER  BOX 

This  drawing  shows  the  top  view,  and  an  isometric  drawing 
of  a  common  miter  box. 

The  oblique  lines,  showing  the  saw  cuts  in  the  isometric  draw- 
ing, are  located  by  laying  off,  on  both  edges  of  the  upper  surface, 
the  measurements  found  from  the  top  view. 

Problem  1. — Draw  the  top  view  of  the  object  as  shown,  and  make  an 
isometric  drawing  with  the  corner  a  at  the  origin  of  the  axes. 

Problem  2. — Draw  the  top  view  of  the  object  as  shown,  and  make  an 
isometric  drawing  with  the  corner  b  at  the  origin  of  the  axes. 


DRAWER  AND  TABLE  JOINTS 

This  drawing  shows  a  unmber  of  joints  such  as  may  be  used 
in  drawer  and  table  constructions. 

Problem  1. — Make  a  drawing  of  the  joints,  showing  A,  B,  and  C  as- 
sembled, omitting  hidden  lines.  Give  all  dimensions. 

Problem  2. — Make  a  drawing  of  the  joints,  showing  D  and  E  assembled, 
omitting  hidden  lines.  Give  all  external  dimensions. 


ISOMETRIC  DRAWING 


101 

PLATE  71 


r 


.3. 


L 


MITER  Box 

a  Scale  4  in.  =  tin. 


,3, 


PLATE  72 


102  MECHANICAL  DRAWING  PROBLEMS 


BOX  WITH  HINGED  LID 

This  drawing  shows  the  end,  and  isometric  views,  of  a  small 
box  with  hinged  lid. 

Since  the  lid  is  partly  opened,  it  will  be  necessary  to  draw 
non-isometric  lines.  These  lines  are  drawn  from  points  located 
by  offsets.  For  illustration:  To  locate  c',  lay  off  a'b'  equal  to 
ab,  and  on  a  vertical  line  drawn  from  b'  lay  off  be,  giving  c'. 
Draw  a  line  from  c'  to/'.  In  a  similar  manner  locate  e'  and  draw 
c'e' '.  To  complete  the  cover,  see  Principle  4,  page  96. 

The  end  view  may  be  drawn  as  shown  for  the  following 
problems. 

Problem  1.— Draw  the  end  view  as  shown,  and  make  an  isometric  drawing 
with  the  corner  m  at  the  origin  of  the  axes.  Omit  hidden  lines. 

Problem  2. — Draw  the  end  view  as  shown,  and  make  an  isometric  draw- 
ing with  the  corner  n  at  the  origin  of  the  axes.  Omit  hidden  lines. 


SAWHORSE 

This  drawing  shows  an  isometric  construction  drawing,  and  an 
isometric  view  of  a  sawhorse. 

The  method  for  finding  the  offsets  required  for  drawing  the 
legs  is  shown  in  the  construction  drawing  and  is  as  follows :  Draw 
the  isometric  axes  and,  using  dimensions  obtained  from  the  iso- 
metric drawing,  lay  off  bg  and  gh.  From  these  points  draw  lines 
parallel  to  the  inclined  axes.  From  6  lay  off  distances  for  c,  d,  f, 
and  e.  Let  bf  and  fe  equal  7,  and  1 1  inches,  respectively.  The 
intersections  of  lines  drawn  parallel  to  the  inclined  axes  from  these 
points  will  give  the  upper  end  of  one  leg,  which  is  completed  by 
drawing  lines  to  the  lower  end,  previously  found.  A  study  of 
the  construction  drawing  should  enable  the  student  to  complete 
the  isometric  drawing. 

Problem  1. — Make  a  construction  drawing,  as  shown,  and  an  isometric 
drawing,  of  the  sawhorse  with  the  point  x  at  the  origin  of  the  axes. 

Problem  2. — Make  a  construction  drawing,  as  shown,  and  an  isometric 
drawing,  of  the  sawhorse  with  the  point  y  at  the  origin  of  the  axes. 


ISOMETRIC  DRAWING 


103 
PLATE  73 


Box  WITH  HINGED  LID 


SAWHORSC 


Construction 
"   Drawing 

Scale  2/'n=fff. 


PLATE  74 


104  MECHANICAL  DRAWING  PROBLEMS 


ISOMETRIC  PRISMS 

This  drawing  shows  the  isometric  views  of  four  right  prisms 
located  from  the  intersections  of  their  axes  as  centers. 

To  make  an  isometric  view  of  a  triangular  prism,  proceed  as 
follows :  Draw  the  top  view  of  the  prism  and  the  axes  xx  and  yy. 
Then  draw  the  isometric  axes  xx  and  yy  and  lay  off  distances  a, 
b,  and  c,  as  found  from  the  top  view,  and  draw  the  base  of  the 
prism  as  shown.  Draw  the  vertical  edges,  measure  the  height 
on  one  edge,  and  complete  the  drawing  by  drawing  lines  parallel 
to  those  of  the  base. 

Problem  1. — Make  a  drawing  of  the  prisms  as  shown.  Let  the  bases  be 
regular  polygons,  the  sides  of  which  are  If,  J,  f,  and  f  inches,  respectively. 
Assume  a  suitable  height  for  the  figures. 

Problem  2. — Make  a  drawing  showing  the  prisms  when  turned  in  a  counter- 
clockwise direction  through  an  angle  of  90°  about  their  central  vertical  axes. 
Assume  suitable  dimensions. 


PRISMS 

This  drawing  shows  the  top  view  and  the  front  view,  also  the 
isometric  drawing,  of  a  pentagonal  prism  resting  on  an  edge  of 
an  hexagonal  prism;  the  pentagonal  prism  making  any  suitable 
angle  with  H. 

To  make  an  isometric  drawing  it  is  necessary  to  draw  the 
front  and  the  top  views  and  substitute  actual  dimensions  instead 
of  the  letters.  From  a  point  o  draw  isometric  axes  and  lay  off 
the  offsets,  as  shown.  A  study  of  the  drawings  should  enable 
the  student  to  execute  the  isometric  view. 

Problem  1. — Make  a  drawing  showing  a  prism  4  inches  long,  the  base 
being  a  regular  pentagon  of  1-inch  sides,  which  rests  on  a  prism  3£  inches 
long,  the  base  being  a  regular  hexagon  of  f-inch  sides.  Assume  a  distance 
for  g,  and  an  angle  for  B. 

Problem  2. — Make  a  drawing  showing  a  prism  4  inches  long,  the  base 
being  an  equilateral  triangle  of  U-inch  sides,  which  rests  on  a  prism  3$ 
inches  long,  the  base  being  a  regular  pentagon  of  1-inch  sides.  Assume  a 
distance  for  g,  and  an  angle  for  6. 


ISOMETRIC  DRAWIXC! 


105 
PLATE  7 


ISOMETRIC    PRISMS 

TOP 


PRISMS 


ORTHOGRAPHIC 
PROJECTION 


PLATE  76 


106  MECHANICAL  DRAWING  PROBLEMS 

ISOMETRIC  CIRCLES 

To  draw  a  true  isometric  circle,  proceed  as  follows:  Draw  a 
circle  showing  the  required  diameter,  circumscribe  a  square,  and 
locate  points  1,  2,  3,  etc.,  as  shown  in  A.  Draw  an  isometric 
square,  as  shown  in  B,  and  locate  points  1,  2,  3,  etc.,  transferred 
from  A  by  measuring  the  distances  parallel  to  the  axes.  Through 
these  points  draw  a  smooth  curve. 

An  approximate  isometric  circle  may  be  drawn  from  four  cen- 
ters as  shown  in  D.  Centers  1  and  2  are  on  the  intersections  of 
lines  drawn  from  a  and  c,  and  perpendicular  to  the  opposite  sides 
of  the  square.  This  is  known  as  the  "four-center"  method. 

A  closer  approximation  to  a  true  ellipse  is  shown  in  E.  In  this 
drawing  eight  centers  are  used.  A  study  of  the  figure  will  enable 
the  student  to  draw  the  circle.  This  is  known  as  the  "eight- 
center"  method. 

Problem  1. — Draw  A,  B,  D,  and  E  as  shown.  Draw  C  similar  to  B, 
and  draw  F  by  the  four-center  method.  Assume  a  suitable  diameter. 

Problem  2. — Draw  A,  B,  D,  and  E  as  shown.  Draw  C  similar  to  B,  and 
draw  F  by  the  eight-center  method.  Assume  a  suitable  diameter. 

ISOMETRIC  ARCS 

This  drawing  shows  approximate  isometric  arcs  drawn  by  the 
four-center  method  for  a  circle.  In  drawing  a  semi-circle,  two 
centers  are  used,  while  for  a  quarter-circle  only  one  center  is 
necessary. 

To  draw  the  arcs  shown  in  A,  proceed  as  follows:  Draw  the 
half-square  fdeag,  and  bisect  da.  From  e  and  g,  draw  lines  per- 
pendicular to  ea  and  ag.  The  intersection  of  these  perpendicu- 
lars gives  the  point  c,  the  center  for  arc  eg.  The  center  for  arc 
ef,  which  lies  on  ec,  is  found  by  drawing  a  line  from  /  perpendicu- 
lar to  df.  Compare  the  letters  in  A,  B,  and  C  with  those  in  D 
of  ISOMETRIC  CIRCLES. 

By  dropping  perpendicular  lines  of  equal  lengths  from  the  cen- 
ters of  arcs  fe,  and  eg,  duplicate  arcs  may  be  drawn.  These  arcs 
will  lie  in  a  plane  parallel  to  the  plane  in  which  arcs  fe  and  eg  are 
drawn.  A  study  of  the  figures  will  enable  the  student  to  work 
the  following  problems. 

Problem  1. — Draw  the  figures  as  shown.  For  dimensions,  measure  the 
drawing  to  a  scale  |  inch  equals  1  inch. 

Problem  2. — Draw  the  figures  shown,  with  the  corners  x  at  the  origin  of 
the  axes.  For  dimensions,  measure  the  drawing  to  a  scale  f  inch  equals 
1  inch. 


ISOMETRIC  DRAWING 


107 
PLATE  77 


ISOMETRIC    CIRCLES 


PLATE  78 


108  MECHANICAL  DRAWING  PROBLEMS 


HOLLOW  CYLINDER 

This  drawing  shows  two  cylinders  drawn  by  the  "eight-center" 
method.  The  letters  in  the  surface  abed,  correspond  to  those 
shown  in  E  of  ISOMETRIC  CIRCLES.  In  drawing  an  object  contain- 
ing concentric  circles,  as  shown  in  B,  it  is  best  to  erase  the  con- 
struction lines  required  for  one  circle  before  the  next  is  begun. 

Problem  1. — Draw  the  cylinders  by  the  four-center  method,  of  the  dimen- 
sions shown,  with  points  c  at  the  origin  of  the  axes. 

Problem  2. — Draw  the  cylinders  by  the  eight-center  method,  of  the  dimen- 
sions shown,  with  points  c  at  the  origin  of  the  axes. 


BEARING  CAP 

This  drawing  shows  the  top  and  the  front  views,  and  the  iso- 
metric drawing  of  a  bearing  cap.  It  illustrates  an  object  con- 
taining concentric  arcs;  also  arcs  in  parallel  planes.  The  arcs  in 
the  vertical  planes  are  quarter-circles.  The  centers  of  the  arcs 
can  readily  be  found  by  referring  to  the  drawings  on  ISOMETRIC 
CIRCLES  and  ISOMETRIC  ARCS. 

Problem  1. — Draw  the  front  and  the  top  views  as  shown,  and  make  an 
isometric  drawing  with  point  x  at  the  origin  of  the  axes. 

Problem  2. — Draw  the  front  and  the  top  views  showing  the  object  in- 
verted, and  make  an  isometric  drawing  with  point  y  at  the  origin  of  the 


ISOMETRIC  DRAWING 


109 
PLATE  79 


HOLLOW     CYLINDER 


B 


Second    Stage 


BEARING     CAP 

ORTHOGRAPHIC    PROJECTION  ISOMETRIC      DRAWING 


PLATE  80 


110  MECHANICAL  DRAWING  PROBLEMS 


MAGNET  POLE  PIECES 

This  drawing  illustrates  two  objects  each  containing  circular 
arcs  in  parallel  planes.  The  object  on  the  left  shows  arcs  in  four 
horizontal  planes.  The  object  on  the  right  contains  arcs  in  two 
parallel  vertical  planes. 

Problem  1. — Make  a  drawing  of  the  objects  with  points  a  at  the  origin 
of  the  axes.  Show  hidden  lines  for  the  bore  in  the  figure  on  the  left.  Omit 
construction  lines  in  both  figures. 

Problem  2. — Make  a  drawing  of  the  objects  with  points  b  at  the  origin  of 
the  axes.  Show  all  hidden  lines  in  the  figure  on  the  right.  Omit  construc- 
tion lines  in  both  figures. 


MILLING  CUTTER  AND  FACE  PLATE 

This  drawing  shows  an  isometric  view  of  a  milling  cutter  having 
sixteen  teeth;  and  a  face  plate  in  part  section,  to  show  its  internal 
construction. 

To  divide  an  isometric  circle  into  any  number  of  equal  parts,  as 
in  the  milling  cutter;  divide  a  true  half-circle  into  half  the  required 
number  of  parts  and  project  these  divisions  to  the  isometric 
circle  as  shown. 

To  draw  the  thread  in  the  face  plate,  draw  three-quarter  circles 
showing  the  beginning  and  the  internal  diameter  of  the  thread. 
On  lines  drawn  from  the  centers  of  the  arcs  found,  and  parallel  to 
the  right  axis,  space  off  a  series  of  points  at  a  distance  apart  equal 
to  the  pitch  of  the  thread.  (For  an  explanation  of  "pitch"  refer 
to  drawings  of  Screw  Threads,  Bolts,  and  Nuts.)  With  these 
points  as  centers  draw  the  remaining  three-quarter  circles. 

Problem  1. — Draw  a  milling  cutter  with  the  dimensions  shown,  and  having 
twenty  teeth. 

Draw  a  full  face  plate  with  dimensions  as  shown. 

Problem  2. — Draw  the  milling  cutter  in  a  vertical  position,  showing  it 
revolved  about  the  axis  ab,  and  having  the  dimensions  shown. 

Draw  the  face  plate  showing  the  face  resting  on  a  horizontal  plane,  and 
of  dimensions  shown.  Assume  a  suitable  section  to  show  the  threads. 


ISOMETRIC  DRAWING 


111 
PLATE  81 


MAGNET  POLE.  PIECES 


MILLING  GUTTER  *ND  FACE 


PLATE  82 


112  MECHANICAL  DRAWING  PROBLEMS 


KNIFE  AND  FORK  BOX 

This  drawing  shows  the  method  of  procedure  for  finding  iso- 
metric views  of  curved  lines. 

To  find  curved  lines,  as  shown  in  A,  proceed  as  follows:  Draw 
vertical  lines  in  A  cutting  the  curved  lines.  Draw  similar  ver- 
tical lines  in  the  isometric  view,  and  from  line  6-6  lay  off  the  dis- 
tance 1-1',  1-1",  3-3',  3-3",  etc.,  equal  to  the  distances  found 
in  A.  Through  the  points  found  draw  smooth  curves.  From 
the  intersections  of  the  vertical  lines  and  the  curves  drawn,  draw 
short  lines  parallel  to  the  left  axis,  as  shown  in  4'-4',  lay  off  dis- 
tances equal  to  the  thickness,  and  draw  smooth  curves. 

Problem  1. — Make  a  drawing  of  the  box  with  point  a  at  the  origin  of  the 
axes.  Scale  6  in.  =  1  ft. 

Problem  2. — Make  a  drawing  of  the  box  with  point  6  at  the  origin  of  the 
axes.  Scale  6  in.  =  1  ft. 


UNIFORM  MOTION  CAM 

This  drawing  shows  the  top  and  the  front  views,  also  the  iso- 
metric drawing  of  an  object  containing  curved  lines,  and  circles, 
which  lie  in  parallel  vertical  planes. 

To  make  an  isometric  drawing  it  is  necessary  to  first  construct 
a  drawing  showing  the  front  and  the  top  views  of  the  object. 

The  curve  egf,  in  the  front  view,  is  found  by  dividing  the  half- 
circle,  also  the  line  de,  each  into  six  equal  parts  and  drawing 
circular  arcs  as  shown.  Through  the  points  of  intersection  of 
the  circular  arcs  and  radial  lines  draw  a  smooth  curve. 

A  study  of  the  drawing  should  enable  the  student  to  work  the 
following  problems. 

Problem  1. — Make  a  drawing  showing  the  top,  front,  and  isometric  views 
of  the  object  with  point  b  at  the  origin  of  the  axes. 

Problem  2. — Make  a  drawing  showing  the  top,  front,  and  isometric  views 
of  the  object  with  point  c  at  the  origin  of  the  axes. 


ISOMETRIC  DRAWING 


113 
PLATE  83 


KNIFE  AND  FORK  Box 

Scale  6in.~  iff. 


Detail  showing  end 


UNIFORM  MOTION  CAM 


PLATE  84 


114  MECHANICAL  DRAWING  PROBLEMS 


CAVALIER  PROJECTION 

Cavalier  projection,  also  called  oblique  projection,  is  somewhat 
similar  to  isometric  drawing  since  it  has  three  axes  on  which 
actual  lengths  are  measured.  One  axis  is  horizontal,  one  vertical, 
and  one  oblique.  The  oblique  axis  may  make  any  angle  with  a 
horizontal;  30°  or  45°  are,  however,  most  generally  used. 

BRACKET  SHELF 

The  drawing  shows  the  object  with  its  oblique  axis  making  an 
angle  of  30°  below  a  horizontal,  thus  showing  a  lower,  or  under- 
neath view. 

Since  one  axis  is  horizontal  and  one  vertical,  the  surface  of 
the  back  is  drawn  in  its  true  shape,  being  parallel  to  the  vertical 
plane  of  projection. 

The  circular  arcs  in  the  bracket  are  drawn  by  the  four-center 
method,  and  the  front  edge  of  the  shelf  is  found  by  offsets  as 
shown  in  the  detail. 

Problem  1. — Make  a  cavalier  projection  of  the  bracket  as  shown. 
Problem  2. — Make  a  cavalier  projection  of  the  bracket  showing  the  front 
and  left  faces,  instead  of  the  front  and  right  as  shown. 

CABINET  DRAWING 

Cabinet  drawing,  also  called  oblique  drawing,  has  three  axes 
on  which  measurements  are  made.  One  axis  is  horizontal,  one 
vertical,  and  one  oblique.  Actual  lengths  are  measured  on  the 
horizontal  and  the  vertical  axes,  and  one-half  actual  lengths  are 
measured  on  the  oblique  axis. 

Drawings  made  by  this  method  show  less  distortion  than  do 
Isometric  Drawings  or  Cavalier  Projections. 

KITCHEN  TABLE 

The  drawing  shows  a  portion  of  the  table  top  removed  to  show 
the  construction  more  clearly.  It  also  shows  the  drawer  partly 
opened. 

Problem  1. — Make  a  cabinet  drawing  of  the  table  showing  the  drawer 
closed.  Scale  2  in.  =  1  ft. 

Problem  2. — Make  a  cabinet  drawing  of  the  table  on  axes  as  shown  in 
B,  thereby  giving  a  view  from  underneath.  Show  the  drawer  pulled  out 
6  inches.  Scale  2  in.  =  1  ft. 


ISOMETRIC  DRAWING 


115 
PLATE  86 


BRACKET  SHELF 


tffe  view  of  bracket  Axes 


KITCHEN  TABLE 

scale'  a  m." i  ft 

Cabinet  Drawing 


Drawer  Details 


PLATE  86 


116  MECHANICAL  DRAWING  PROBLEMS 


KNUCKLE  JOINT 

This  drawing  shows  an  object  containing  a  number  of  circles 
and  circular  arcs  in  parallel  vertical  planes;  also  a  number  of 
circular  arcs  in  horizontal  planes. 

The  circles  and  arcs  in  the  vertical  planes  are  drawn  with  the 
compass.  The  arcs  in  the  horizontal  planes  must  be  drawn 
through  points  plotted  from  the  top  view  shown  below. 

Problem  1. — Draw  a  top  view  and  make  a  cabinet  drawing  of  the  object 
as  shown. 

Problem  2. — Draw  a  top  view  and  make  an  assembly  cabinet  drawing  of 
the  object  showing  the  bolt  in  place. 


SMALL  BENCH 

An  object  may  be  revolved  into  any  number  of  positions  and 
still  show  three  faces. 

The  object  shown  in  the  drawing  is  revolved  to  a  position  so 
that  the  axes  make  angles  as  shown  in  the  axes  diagram. 

The  arches  shown  in  the  legs  are  half-circles  and  may  be  drawn 
as  shown  by  the  two  figures  on  the  left;  while  the  quarter-circles 
in  the  top  are  isometric  quarter-circles. 

Problem  1. — Make  a  drawing  showing  the  object  with  a  at  the  origin 
of  the  axes.  Let  the  left  axis  make  an  angle  of  45°,  and  the  right  axis  an 
angle  of  15°,  with  a  horizontal. 

Problem  2. — Make  a  drawing  showing  the  object  with  b  at  the  origin  of 
the  axes.  Let  the  left  axis  make  an  angle  of  7°,  and  the  right  axis  an  angle 
of  41°,  with  a  horizontal.  Measure  actual  lengths  on  the  left  and  the  ver- 
tical axes,  and  one-half  actual  lengths  on  the  right  axis. 

NOTE. — Since  the  width  of  the  object  is  reduced  to  half  the  actual  dimen- 
sions the  arcs  in  legs  and  top  cannot  be  drawn  with  the  compass  but  must 
be  plotted  by  offsets,  as  shown  in  the  drawing  of  the  KNIFE  AND  FORK 
Box. 


ISOMETRIC  DRAWING 


117 
PLATE  87 


KNUCKLE  JOINT 


SMALL    BENCH 

AXONOMETR/C    DRAWING 


PLATE  88 


118  MECHANICAL  DRAWING  PROBLEMS 

SECTION  IV 
MACHINE  DETAILS 

Cast  Iron 

ECCENTRIC  SHEAVE 

The  drawing  shows  a  front  view  and  an  incomplete  side  view. 
The  latter  is  to  be  completed  when  working  the  problems.  The 
distance  a  is  the  eccentricity,  or  throw,  and  is  equal  to  one-half 
the  valve  travel. 

The  following  proportions  are  for  eccentrics  to  5  inches  valve 
travel  : 

D  =  diameter  of  shaft     /  =  D  +  ^  I  =  e  —  % 

a  =  throw  g  =  2JD  -  ^  m  =  2e  —  ^§ 

b  =  \$D  h  =  ie  +  &  *  -  fc  -  J 

c  =  2JD  j  =  \e  -  |  o  =  \e  +  & 

e  =  £D  +  |  k  =  e-&  P  =  i*  -  A 

Problem  1.  —  Make  a  drawing  of  an  eccentric  sheave  for  a  2-inch  shaft 
and  f-inch  throw.  Draw  full  size. 

Problem  2.  —  Make  a  drawing  of  an  eccentric  sheave  for  a  4^-inch  shaft 
and  2g-inch  throw.  Scale  6  in.  =  1  ft. 

Problem  3.  —  Assume  a  value  for  shaft  diameter  and  a  throw  for  an  ec- 
centric sheave,  and  draw  two  views. 

Machine 
HAND-WHEEL 

The  drawing  shows  a  full  cross-section  and  an  incomplete  front 

view.     The  latter  is  to  be  completed  when  working  the  problems. 

To  construct  an  arm,  draw  straight  line  5-6  giving  point  7. 

Through  point  7  draw  a  line  making  angle  6-7-8  equal  to  angle 

7-6-8,  giving  centers  8  and  9.     From  these  centers  the  center- 

line  of  the  arm  may  be  drawn.     The  centers  for  the  arcs,  giving 

the  thickness  of  the  arm,  must  lie  on  line  9-8,  and  are  to  be  found 

by  trial.     Omit  all  construction  lines  in  the  drawing  when  inking. 

The  following  proportions  are  for  wheels  up  to  12  inches  diam- 

eter: 

A  =  diameter  of  wheel   e  =  \A  —  &  i  =  -&A  +  •& 


d  =  &A+$  h  =  2d   -  f  l  =  \j 

Problem  1.  —  Make  a  drawing  for  a  5-inoh  hand-wheel  with  four  arms. 

Draw  full  size. 
Problem  2.  —  Make  a  drawing  for  a  10-inch  hand-wheel  with  six  arms. 

Scale  6  in.  =  1  ft. 
Problem  3.  —  Assume  a  diameter  for  a  hand-wheel  and  draw  two  views. 


MACHINE  DETAILS 


119 
PLATE  89 


CAST  IRON 

ECCENTRIC  SHEAVE 


Section  3-4- 


MACHINE: 

HAND-WWEEL 

PLATE  90 


120  MECHANICAL  DRAWING  PROBLEMS 

Design  of 
ENGINE  CRANK 

Cranks,  like  eccentrics,  are  devices  used  for  transforming  rotary 
motions  into  reciprocating  motions.  They  are  sometimes  made 
of  cast  iron,  but  usually  of  cast  steel  or  machine  steel. 

The  lines  of  intersection  in  the  side  view  are  found  by  assuming 
points  on  the  fillets,  projecting  to  the  front  view  and  back  to  the 
side  view,  as  indicated  by  the  direction  of  the  arrows  in  the  lower 
curve. 

A  =  throw  of  crank  /  =  |D  +  ^  I  =  %D  +  3 

D  =  diameter  of  shaft  g  =  D  m  =  D  —  \ 

b  =  \\D  h  =  &D  +  |  n  =  \D 

c  =  1|Z)  +  I  j  =  HD  +  J  p  =  \D  +  & 

Problem  1. — Make  a  drawing  of  a  crank  for  43-inch  throw  and  IJ-inch 
shaft.  Draw  full  size. 

Problem  2. — Make  a  drawing  of  a  crank  for  7-inch  throw  and  23-inch 
shaft.  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  values  for  A  and  D  and  draw  two  views  of  a  crank. 

Machine  Steel 
CONNECTING-ROD  END 

Connecting-rods  are  used  'in  steam  engines  to  join  the  crank 
with  the  cross-head;  also  in  gasoline  engines  to  connect  the  piston 
with  the  crank  shaft.  They  convert  the  reciprocating  motion  of 
the  piston  to  a  rotary  motion  of  the  shaft.  Connecting-rods  are 
made  of  machine  steel,  although  for  some  types  of  small  gasoline 
engines  they  may  be  made  of  bronze. 

The  drawing  shows  the  cross-head  end,  or  piston  end,  of  a 
solid  rod.  The  hole,  when  the  rod  is  made  of  steel,  is  lined  with 
white  metal  or  bronze.  This  lining  is  called  a  "bushing,"  and  is 
frequently  made  about  f  inch  thick. 

D  =  outside  diameter  of  bushing  c  =  IfD  +  & 

a  =  l\D  +  &  d  =  2D  +  J 


Problem  1. — Make  the  drawing  for  a  connecting-rod  end  when  the  outside 
diameter  of  the  bushing  is  If  inches.  Draw  full  size. 

Problem  2. — Make  the  drawing  for  a  connecting-rod  end  when  the  outside 
diameter  of  the  bushing  is  3  inches.  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  a  value  for  D  and  draw  three  views  of  a  connecting- 
rod  end. 


MACHINE  DETAILS 


121 
PLATE  91 


—  0  - 

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-   -C     — 

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i 

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^ 

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[             !      ' 
I  Q    -Q   - 

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^ 

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T( 

1 

V, 

7   — 

DESIGN  or 

ENGINE  CRANK 


MACHINE:  STEEL 
CONNECTING-ROD  END 


PLATE  92 


122  MECHANICAL  DRAWING  PROBLEMS 

Soft  Steel 
CRANE  HOOK 

Cranes  are  machines  used  for  hoisting  or  lowering  weights,  and 
crane  hooks  are  attached  to  these  machines  by  means  of  a  steel 
cable  or  rope  for  holding  or  sustaining  the  weights.  The  hooks 
are  generally  made  of  soft  steel. 

The  drawing  shows  the  front  view,  the  side  view,  and  three 
cross-sections  of  a  hook. 

a  =  throat  opening  /  =  .7  a  k  =  .85  a 

b  =  5.4  a  g  =  1.2  a  I  =  .9  a 

c  =  1.5  a  h  =  .85  a  m  =  .2  a 

d  =  1.5  a  i  =  .1  a  n  =  .6  a 

e  =  .2  a  j  =  .8  a  o  =  .8  a 

Problem  1. — Make  a  drawing  showing  two  views  and  sections  for  a 
crane  hook  having  a  l|-mch  throat  opening.  Draw  full  size. 

Problem  2. — Make  a  drawing  showing  two  views  and  sections  for  a 
crane  hook  having  a  2J-inch  throat  opening.  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  the  throat  opening  for  a  crane  hook  and  draw  two 
views  and  sections,  as  shown. 

Cast  Iron 
CLUTCH  COUPLINGS 

Clutch  couplings  are  used  for  connecting,  or  for  disconnecting, 
two  shafts.  They  are  generally  made  of  cast  iron. 

The  drawing  shows  a  square  jaw  coupling,  also  a  spiral  jaw 
coupling,  each  having  four  jaws.  The  left  hand  portions  are 
keyed  to  the  shafts;  the  right  hand  portions  are  movable  and 
are  prevented  from  turning  on  the  shafts  by  feather  keys.  The 
end  views  are  shown  incomplete  in  the  drawing. 

D  =  diameter  of  shafts  e  =  1%D  +  %  j  =  &D  +  & 

a  =  2D  +  1  /  =  \D  k  =  &D  +  & 

b  =  IfD  +  If  g  =  |D  +  |  I  =  g  +  J 

c  =  UD  +  i  h  =  \\D  +  f  m  =  l\D  +  1 

Problem  1. — Make  a  drawing  showing  front  and  end  views  of  a  square 
jaw  coupling,  also  of  a  spiral  jaw  coupling,  each  having  four  jaws.  Let 
D  =  1  inch.  Draw  full  size. 

Problem  2. — Make  a  drawing  showing  front  and  end  views  of  a  square 
jaw  coupling,  also  a  spiral  jaw  coupling,  each  having  three  jaws.  Let 
D  =  If  inches.  Show  each  in  half  section.  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  ft  diameter  for  D  and  draw  two  views  of  a  square 
jaw  coupling,  also  a  spiral  jaw  coupling,  each  having  four  jaws. 


MACHINE  DETAILS 


123 
PLATE  93 


SOFT  STEEL 

CRANE  HOOK 


CAST  IRON 

CLUTCH  COUPLINGS 


PLATE  94 


124  MECHANICAL  DRAWING  PROBLEMS 

SCREW  THREADS,  BOLTS  AND  NUTS 

Screws,  bolts,  studs,  and  nuts  are  used  in  all  machines  to  a 
greater  or  less  extent.  A  knowledge  of  their  proportions  and 
their  conventional  representation  is  a  prime  requisite  of  draftsmen 
engaged  in  machine  drawing. 

The  exact  representation  of  a  screw  thread  is  a  laborious  and 
time-consuming  operation,  since  the  curve  of  a  thread  is  a  helix 
which  is  plotted  by  projecting  points  from  an  end  view.  In 
practice  it  is  not  often  necessary  to  draw  exact  threads;  therefore, 
to  economize  in  time  the  threads  are  conventionalized  and  shown 
by  straight  lines. 

The  distance  between  two  successive  threads  on  a  screw  is 
called  the  "pitch;"  that  is,  the  pitch  is  the  distance  a  screw  will 
advance  in  the  direction  of  its  axis  in  one  revolution. 

The  drawings  show  accepted  conventions  for  representing 
screw  threads.  The  conventions  in  the  upper  drawing  are  suit- 
able for  screws  of  three-quarter  inch  and  less  in  diameter.  The 
lower  drawing  shows  conventions  for  screws  of  larger  diameters. 

In  drawing  a  conventional  screw  it  is  not  necessary  to  show 
the  exact  number  of  threads  per  inch.  The  diameter  fixes  the 
number  of  threads,  since  screws  are  made  "standard,"  and  defi- 
nite diameters  have  a  definite  number  of  threads  per  inch.  If 
a  non-standard  screw  is  necessary  in  a  machine,  the  number  of 
threads  per  inch  should  be  stated  in  a  note  on  the  drawing. 

Consult  the  tables  on  screws,  bolts,  and  nuts  for  proportions, 
and  see  Figs.  33  and  34  for  drawing  threads. 

Conventions  for 
SCREW  THREADS 

Problem  1. — Make  a  drawing  as  shown.     Assume  suitable  diameters  for  d. 
Problem  2. — Make  a  drawing  as  shown.     Let  the  diameters  equal  f, 
f>  f>  %>  •&>  ^nd  I  inches,  respectively. 

Conventions  for 
BOLTS  AND  NUTS 

Problem  1. — Make  a  drawing  as  shown.     Assume  suitable  diameters  for  d. 
Problem  2. — Make  a  drawing  as  shown.     Let  the  diameters  equal  1, 
|,  f,  f,  and  |  inches,  respectively. 


MACHINE  DETAILS 


125 
PLATE  95 


Cap  Screws 


CONVENTIONS  FOR 

SCREW  THREADS 


Cap    Screws 


UJ 


CONVENTIONS  FOR 

BOLTS  AND  NUTS 


PLATE  96 


126  MECHANICAL  DRAWING  PROBLEMS 

Drop  Forged 
LATHE  CARRIER 

Lathe  carriers,  frequently  called  lathe  dogs,  are  tools  used  for 
driving  mandrels  in  engine  lathes.  The  mandrel  supported  by 
the  lathe  centers  is  driven  by  the  carrier,  which  is  fixed  to  one 
end  by  a  set  screw.  The  carrier  is  driven  by  the  face  plate  of 
the  lathe.  Lathe  carriers  may  be  made  of  cast  iron,  cast  steel, 
or  drop  forgings. 

The  drawing  shows  the  top  view,  the  end  view,  and  the  center 
line  for  the  front  view.  The  shape  of  the  curve  in  the  top  view, 
on  which  two  points  are  shown  by  4-4,  may  be  found  as  in  pre- 
vious problems. 

A  =  diameter  of  opening     e  =  &A  j  =  \A  —  ^ 

6  =  4A  -  i  /  =  U  -  A  k  =  \A  +  & 

c  =  \\A  -  &  g  =  A  -  t  I  =  U  -  A 

d  =  HA  -  A  A  =  U  +  A  m  =  \A 

Problem  1. — Make  a  drawing  showing  three  views  of  a  carrier  when  A 
equals  If  inches.  Draw  full  size. 

Problem  2. — Make  a  drawing  showing  three  views  of  a  carrier  when 
A  =  3  inches.  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  a  diameter  for  A  and  draw  three  views  of  a  carrier. 

Cast  Iron 
CLAMP  COUPLING 

Clamp  couplings,  also  called  split  couplings,  are  used  for  con- 
necting the  ends  of  shafts.  There  are  many  forms  of  couplings; 
the  one  shown  is  generally  used  in  cramped  places.  They  are 
almost  always  made  of  cast  iron. 

The  coupling  in  the  drawing  is  provided  with  a  keyway.  The 
insertion  of  keys  prevents  the  shafts  from  turning  in  the  coupling. 
The  views  are  shown  incomplete. 

D  =  diameter  of  shaft  e  =  f  6  +  &  I  =  \J>  +  & 

a  =  2D  +  S$  /  =  le  -  A  TO  =  31^+  ^ 

b  =  2D  +    f  g  =  J6  +  A  n  =  ID 

c  =  la  h  =  1J0  -  H  a  =  In  +  &• 

d  =  a-2c  k  =  1  +  &  P  =  Aa  +  ^ 

Problem  1. — Make  a  drawing  showing  three  complete  views  for  a  11- 
inch  coupling  containing  four  bolts.  Draw  full  size. 

Problem  2. — Make  a  drawing  showing  three  complete  views  for  a  21- 
inch  coupling  containing  four  bolts.  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  a  shaft  diameter  for  a  clamp  coupling  and  draw 
three  views. 


MACHINE  DETAILS 


127 
PLATE  97 


LTTJ 


DROP  FORCED 

LATHE  CARRIER 


CAST  IRON 

CLAMP  COUPLING 


PLATE  98 


128  MECHANICAL  DRAWING  PROBLEMS 

Piston  Rod 
STUFFING  BOX 

Stuffing  boxes  are  used  on  engines,  pumps,  and  many  other 
machines,  to  prevent  leakage  of  steam,  water,  etc.  They  are 
usually  made  of  cast  iron  with  two  or  more  parts  of  bronze  encir- 
cling the  movable  rod. 

The  drawing  shows  a  stuffing  box  suitable  for  steam  engines. 
The  outer  part,  or  box,  is  cast  iron,  while  the  two  parts,  called 
glands,  encircling  the  rod,  are  bronze.  Leakage  is  prevented  by 
filling  the  cavity  a  with  an  elastic  substance  which  is  pressed 
against  the  rod  by  the  outer  gland.  The  outer  gland  is  forced  into 
the  box  by  screwing  down  the  nuts. 

D  =  diameter  of  rod  g  =  &D  +  If  n  =  if  D  +  ri 

a  =  D  +  I  h  =  &D  +  A  o  =  1|D  +  1| 

b=D  +  tf  J  =  ID  +  H  p  =  iD  +  & 

c  =  D  +  &  k  =  D  +  1  g  =  1JD  +  U 

e  =  HZ)  +  H  I  =  \D  +  i  r  =  AD  +  A 

/  =  ID  +  2*  »»  =  jz>  +  & 

Problem  1. — Draw  front  and  end  views  of  a  stuffing  box  for  a  f-inch  rod. 
Show  the  front  view  in  half-section.  Draw  full  size. 

Problem  2. — Draw  two  views  of  a  stuffing  box  for  a  2-inch  rod.  Show 
the  front  view  in  full-section.  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  a  diameter  for  D  and  draw  two  views  of  a  stuffing 
box. 

Flanged 

SAFETY  COUPLING 

Couplings  are  frequently  provided  with  a  flange  or  rim  at  their 
outer  edge  to  prevent  accidents  which  might  occur  by  a  belt  or  a 
person's  clothing  becoming  entangled  with  the  bolts.  Couplings 
of  this  type  are  made  of  cast  iron. 

D  =  diameter  of  shaft     /  =  f  a  o  =  3  «  +  A 

a  =  4D  g  =  -ka  +  &  p  =  \D 

6  =  2£D  -  i  h  =  jia  +  &  q  =  $P  +  t 

c  =  UD  +  i  l  =  &a  +  &  r=c+h 

d  =  $D  +  1  w  =  if  a  —  }  s  =  c  -  g 

e  =  -ha  +  &  n  =  &a  +  -& 

Problem  1. — Make  a  drawing  showing  two  views  for  a  IJ-inch  coupling. 
Show  in  half-section  with  all  bolts  which  are  visible.  Draw  full  size. 

Problem  2. — Make  a  drawing  showing  two  views  for  a  3-inch  coupling 
with  six  bolts.  Show  in  half -section .  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  a  shaft  diameter  for  a  safety  coupling  and  draw  two 
views.  Show  with  the  shafts  removed. 


MACHINE  DETAILS 


129 
PLATE  99 


PISTON  ROD 

STUFFING   Box 


FLANGED 

SAFETY  COUPLING 


PLATE  100 


130  MECHANICAL  DRAWING  PROBLEMS 

Cast  Iron 
NUT  COUPLING 

Nut  couplings  may  be  used  on  rods  whose  lengths  it  may  be 
desirable  to  vary  within  certain  limits.  Couplings  of  this  kind 
may  be  made  of  cast  iron,  steel,  or  bronze. 

The  drawing  shows  a  nut  coupling  which  allows  a  rod,  consist- 
ing of  two  parts,  to  be  lengthened  or  shortened.  One  part 
screws  into  the  coupling  with  a  right-hand  thread ;  the  other  part 
screws  into  the  coupling  with  a  left-hand  thread. 

Study  the  drawing  for  method  of  finding  the  lines  of  intersection. 
D  =  diameter  of  rod        e  =  l\D  +  1  k  =  D  +  f 

a  =  4D  /  =  !?£>  +  !  m  =  &a  +  J 

b  =  HD  +  If  g  =  &a  -  |  n  =  fa  -  \ 

c  =  |a  +  J  h  =  Aa  +  2f  p  =  -&D  +  & 

d  =  f  a  -  | 

Problem  1. — Draw  three  views  of  a  nut  coupling  for  a  If-inch  rod.  Show 
one  view  in  full-section.  Draw  full  size. 

Problem  2. — Draw  three  views  of  a  nut  coupling  for  a  2^-inch  rod.  Show 
one  view  in  half-section.  Scale  6  in.  =  1  ft. 

Problem  3. — Assume  a  rod  diameter  for  a  nut  coupling  and  draw  three 
views.  Show  a  section  in  one  view. 

Machine  Steel 
FORKED  COUPLING 

Forked  rods  are  sometimes  used  for  the  cross-head  end  of  con- 
necting rods  for  steam  engines.  Similar  rods  are  also  used  in  a 
variety  of  machines.  The  jaws  may  be  solid,  or  they  may  be 
provided  with  caps  as  shown.  They  are  always  made  of  steel. 

The  jaws  on  the  rod  in  the  drawing  are  provided  with  caps 
which  are  fastened  to  the  jaws  by  means  of  cap  screws.  (See 
table  for  proportions  of  cap  screws.) 

Study  the  drawing  for  method  of  finding  the  various  lines  of 
intersection  in  the  lower  jaw. 

D  =  diameter  of  bore      /  =  Ife  —  ff  m  =  fa  —  -^ 

a  =2D  ff  =  f  e  -  H  n  =  Ja  +  J 

6  =  5Z>  -  2f  h=f-g  0=ia-^ 

c  =  D  -  A  i  =  *a  +  !  P  =  ia  -  & 

d  =  \%D  -  |  k  =  ia  +  H  q  =  $a  -  J 

e  =  2D  -  J  Z  =  ia-i  r  =  n  -  A 

s  =r  +  & 

Problem  1. — Make  a  drawing  showing  three  views  of  a  rod  for  a 
11 -inch  bore.  Draw  full  size. 

Problem  2. — Draw  three  views  of  a  rod  for  a  2|-inch  bore.  Scale  6 
in.  =  1  ft. 

Problem  3. — Assume  a  bore  for  a  forked  rod  and  draw  three  views. 


MACHINE  DETAILS 


131 
PLATE  101 


R.H.Th. 


CAST  /RON 

NUT  COUPLING 


e  -—»T  o  "x^ \J.-"'' 


MACHINE  STEEL 

FORKED  ROD 


PLATE  102 


132  MECHANICAL  DRAWING  PROBLEMS 

Clutch  Coupling 
SHIFTING  GEAR 

Shifting  gears  are  employed  in  engaging  or  disengaging  coup- 
lings and  clutches,  and  for  moving  belts  from  tight  or  loose  pul- 
leys or  vice  versa. 

For  D  see  Clutch  Couplings,  page  122. 

*  =  1H  +  & 

y       to  be  assumed 
Problem  1. — Make  a  drawing  as  shown.    Let  D  =  1  and  y  =  5  inches. 

Draw  full  size. 

Problem  2. — Make  a  drawing  as  shown  having  the  lower  half  of  the  collar 

in  section.     Let  D  =  If  and  y  =  8f  inches.     Scale  6  in.  =1  ft. 

Problem  3. — Make  a  drawing  as  shown.     Assume  dimensions  for  D 

and  y,  also  assume  a  suitable  section. 

Buttress-Thread 
PLANER  JACK 

-  Planer  jacks  are  frequently  used  on  the  beds,  or  tables,  of  plan- 
ing machines,  milling  machines  or  boring  machines,  to  assist  in 
holding  or  supporting  machine  parts  which  are  to  be  planed, 
milled  or  bored.  They  are  made  with  a  cast  iron  base  or  nut,  and 
a  soft  steel  screw  and  cap. 

The  drawing  shows  the  top  view,  the  front  view,  and  the  center 
line  for  the  side  view  of  a  jack  with  a  buttress-thread  screw. 
Square-thread  screws  are  also  frequently  used. 

D  =  diameter  of  screw   h  =  ID  +  &  p  =  \D 

b  =  2\D  +  A  k  =  %D  s  =  |D  -  & 

c  =  HD  +  i  I  =  3|D  +  &  t  =  f  D  +  & 


17  =  D  o  =  ID  +  A 

Problem  1. — Draw  three  views  and  details  of  a  planer  jack  with  buttress- 
thread  screw  of  |-inch  pitch.  Let  D  =  f  inch.  Draw  full  size. 

Problem  2. — Draw  three  views  and  details  of  a  planer  jack  with  a  square- 
thread  screw  of  Hnch  pitch.  Let  D  -  1  inch.  Scale  6  in.  =  1  ft. 

Problem  3. — Make  a  drawing  showing  three  views  and  necessary  details 
for  a  planer  jack  having  a  square-thread  screw.  Assume  a  pitch  and  a 
diameter  for  the  screw. 


MACHINE  DETAILS 


133 
PLATE  103 


jf&. 


CLUTCH   COUPLING 

SHIFTING  GEAR 


BUTTRESS  THREAD 

PLANER  JACK 


PLATE  104 


134  MECHANICAL  DRAWING  PROBLEMS 

Single-Curve  Arm 

BELT  PULLEY 

To  find  the  center  for  one  curve  of  an  arm  as  shown  proceed  as 
follows:  From  x  and  z  draw  30°  lines  intersecting  at  1,  an$  from  1 
as  center  draw  arc  xyz.  Lay  off  d  and  d',  giving  points  2-3  and 
4-5.  Draw  line  2-3.  From  3  draw  a  line  making  angle  6-3-2 
equal  angle  1-2-3,  giving  point  7,  the  center  for  curve  2-3.  The 
center  for  curve  4-5  is  found  similarly. 

A  =  diameter  of  pulley  a  =  2C  d'  =  \d 

i/ 

B  =  width  of  face  6  =  \B  e  =  4 

C  =  diameter  of  bore  c  =  .005£  +  .03      /  =  —5  +  i 

N  =  number  of  arms  d  =  .63\|-^-  g  =  f  inch  tap 

Problem  1.  —  Make  a  drawing  of  a  pulley  with  five  arms.  Let  A  =  9,  B  — 
1\  and  C  —  \\  inches.  Draw  full  size. 

Problem  2.  —  Make  a  drawing  of  a  pulley  with  six  arms.  Let  A  =  16,  B  = 
4£  and  C  =  2  inches.  Scale  6  in.  =1  ft. 

Problem  3.  —  Make  a  drawing  of  a  20-inch  pulley  having  a  5-inch  face, 
2^-inch  bore,  and  six  straight  arms. 

Double-Curve  Arm 

BELT  PULLEY 

To  find  the  centers  for  the  arcs  of  the  lower  part  of  an  arm  as 
shown  proceed  as  follows:  Draw  45°  lines  through  x,  y,  z,  and 
draw  arcs  xy  and  yz.  Lay  off  d  and  d",  giving  points  1-2  and 
3-4.  From  3,  on  line  ran,  lay  off  a  distance  equal  to  1-5,  giving 
point  6,  the  center  for  curve  1-3.  From  4,  on  line  ran,  lay  off  a 
distance  equal  to  2-5,  giving  point  7,  the  center  for  curve  2-4. 
The  centers  for  the  upper  part  of  the  arm  are  found  similarly. 
A  =  diameter  of  pulley  a  =  2C  d"  =  \d 

B  =  width  of  face  V  =  \B  e  =  ^ 

C  =  diameter  of  bore          c  =  .0055  +  .03  /  =  ~  +  f 

N  =  number  of  arms          d  =  .63  V  h  =  1  inch  drill 


Problem  1.  —  Draw  two  views  of  a  pulley  having  five  arms  similar  to  those 
shown.  Let  A  =  9,  B  =  2  and  C  =  1  J  inches.  Draw  full  size. 

Problem  2.  —  Draw  two  views  of  a  pulley  having  six  arms  similar  to  those 
shown.  Let  A  =  18,  B  =  4£  and  C  =  2  inches.  Scale  6  in.  =  1  ft. 

Problem  3.  —  Draw  two  views  of  a  36-inch  pulley  having  a  9-inch  face, 
3-inch  bore,  and  six  arms  similar  to  those  shown. 


MACHINE  DETAILS 


135 
PLATE  106 


Taper  -for  Hub  and  Rim  Arm    Section 


SINGLE-CURVE  ARM 

BELT  PULLEY 


Taper  far 
Hub  and  Rim 


DOUBLE-CURVE  ARM 

BELT  PULLEY 


PLATE  106 


136  MECHANICAL  DRAWING  PROBLEMS 

Compression 
GREASE  CUP 

Grease  cups  are  receptacles  for  holding  heavy,  viscid  lubri- 
cants. They  are  placed  near  or  on  top  of  bearings,  such  as  engine 
bearings,  shaft  bearings,  etc.,  to  provide  a  means  for  lubrication. 
Grease  cups  are  generally  made  of  brass,  although  cheap  grades 
are  made  of  iron  or  steel.  They  are  always  provided  with  a  pipe- 
thread  for  fastening  to  the  bearing. 

a  =  depth  of  body          j  =  -^a  +  f  s  =  ff  a  +  f 

&  =  fa  +  i  *  =  Aa  +  A  <  =  fa  +  i 

c  =  Ha  +  M  I  =  Ha  +  |  u  =  Aa  +  A 

d  =  Ma  +  f  TO  =  ia  +  H  '  »  =  *a  +  A 

e  =  Ifa  +  |  «  =  Aa  +  A  w  =  &a  +  & 


(7  =  tta  +  A  2  =  ft  a  +  A 

r  =  ^a  +  | 

Problem  1.  —  Draw  a  grease  cup  and  details  as  shown.  Let  a  =  2i 
inches,  and  y'  =  |-inch  pipe  thread.  Draw  full  size. 

Problem  2.  —  Draw  the  assembled  view  of  a  grease  -cup  in  half  -section, 
and  the  details  as  shown.  Let  a  =  4  inches,  and  y'  =  Hnch  pipe  thread. 
Scale  6  in.  =  1  ft. 

Problem  3.  —  Assume  a  value  for  a  and  a  diameter  for  the  pipe  thread,  and 
make  the  necessary  views  for  a  working  drawing  of  a  screw-feed  grease  cup. 

Adjustable 
LATHE  CHUCK 

Lathe  chucks  are  devices  which  are  screwed  to  the  spindles  of 
lathes  and  are  used  for  holding  materials  to  be  turned,  bored  or 
drilled.  The  drawing  shows  an  adjustable  chuck  suitable  for  use 
on  a  wood-turning  lathe. 

a  =  diameter  of  spindle  thread       TO  =  10  threads  per  inch 

b  =  length  of  spindle  thread  n  =  diameter  of  drill  for  No.  12  screw 

c  =  number  of  threads  per  inch 

d  =a  +  f  ft  =  i  <Z  =  b  +  !  M  =  I 

0  =  b  +  A  k=a+&  r=d+%  v=k 

/  =  A  I  =  6  +  i  *  =3-  A  *>  =  A 


Problem  1.  —  Make  an  assembled  drawing  for  a  chuck,  and  draw  details 
as  shown.  Let  a  =  1J  inches,  b  =  If  inches,  and  c  =  8  threads  per  inch. 

Problem  2.  —  Make  an  assembled  drawing  for  a  chuck  in  half  -section,  and 
draw  details  as  shown.  Let  a  =  If  inches,  6  =  U  inches,  and  c  =  8 
threads  per  inch. 

Problem  3.  —  Measure  the  spindle  of  a  lathe  for  a,  b,  and  c,  and  make  a 
working  drawing  for  an  adjustable  chuck  as  shown. 


MACHINE  DETAILS 


137 
PLATE  107 


Core 


Face  Plate 


ADJUSTABLE 

LATHE  CHUCK 


PLATE  108  g 


138  MECHANICAL  DRAWING  PROBLEMS 

PIPE  UNIONS 

Pipe  unions  are  metallic  fittings  used  to  join  sections  of  pipe;  as 
water  pipe,  gas  pipe,  steam  pipe,  etc.  They  may  be  classified 
as  nut  unions  and  flange  unions.  Nut  unions  are  generally  used 
for  pipes  to  2  inches  diameter,  and  flange  unions  for  pipes  above  2 
inches,  although  nut  unions  for  pipes  to  4-inch  diameter  may  be 
obtained.  Nut  unions  are  made  of  malleable  iron,  malleable  iron 
and  brass,  and  all  brass.  Flange  unions  are  made  of  cast  iron. 

Spherical  Seat 
PIPE  UNION 

This  drawing  shows  a  nut  union  with  a  spherical  seat.  The 
seat  is  made  of  two  brass  rings  which  are  accurately  ground  to 
insure  a  tight  joint. 

D  =  diameter  of  pipe      /  =  1  &D  +  &  I  =  fZ)  +  ^ 


™ 


d  = 
e  = 


Problem  1.  —  Make  a  drawing  showing  an  assembly  section,  and  details 
of  a  nut  union  for  a  1-inch  pipe.  Draw  full  size. 

Problem  2.  —  Make  a  drawing  showing  an  assembly  in  half-section,  and 
details  in  full-section  of  a  nut  union  for  a  2-inch  pipe.  Scale  6  in.  =1  ft. 

Problem  3.  —  Assume  a  pipe  diameter  and  make  a  working  drawing  for  a 
nut  union  with  a  spherical  seat. 

Gasket  Seat 
PIPE  UNION 

This  drawing  shows  a  nut  union  with  a  gasket  seat.  Gaskets 
are  generally  made  of  a  rubber  composition,  or  of  asbestos.  They 
insure  a  tight,  non-leaking  joint. 

D  =  diameter  of  pipe  e  =  l&D  +  f  j  =  \D  +  } 

a  =  1JZ)  +  H  /  =  IAD  +  f  k  =  \D  +  | 

6  =  iZ>  +  f  0  =  UZ>  +  A  z  =  Al>  +  i 

c  =  |Z>  +  1  h  =  D  m  =  l&D  +  A 


Problem  1.  —  Make  a  drawing  showing  front,  top,  and  end  views  of  a 
nut  union  for  a  1-inch  pipe.  Show  front  and  top  views  in  half-section. 

Problem  2.  —  Make  a  drawing  showing  three  views  of  a  nut  union  for  a 
2-inch  pipe.  Assume  suitable  sections.  Scale  6  in.  =  1  ft. 

Problem  3.  —  Assume  a  pipe  diameter,  and  make  a  working  drawing  for  a 
nut  union  with  a  gasket  seat. 


MACHINE  DETAILS 


139 
PLATE  109 


r 


:!>~ 


SPHERICAL    SEAT 

PIPE  UNION 


CASKET    SEAT 

PIPE  UNION 


PLATE  110 


140  MECHANICAL  DRAWING  PROBLEMS 

Square  Thread 
SCREW  JACK 

Screw  jacks  are  portable  devices  used  for  lifting  heavy  loads 
through  short  distances.  To  raise  a  load,  the  screw  is  turned  with 
a  bar  inserted  into  the  holes  of  the  screw  head. 

The  drawing  shows  a  simple  screw  jack.  It  consists  of  a 
square-threaded  steel  screw  working  in  a  cast  iron  body  or  nut. 

Problem  1. — Make  an  assembly  drawing  with  details  for  a  jack  as  shown. 
Let  a  =  4J  inches  and  6  =  6  inches.  Draw  full  size. 

Problem  2. — Make  an  assembly  drawing  as  shown,  and  draw  details  of 
the  screw,  bearing  plate,  and  bearing  plate  screw.  Let  a  =  6  inches  and 
6  =  7£  inches.  Draw  full  size. 

Problem  3. — Multiply  the  dimensions  shown  by  1.5  and  make  an  assembly 
drawing  for  a  jack  with  a  buttress-thread  screw  of  one-eighth  pitch,  and 
draw  details  of  the  screw,  bearing  plate,  and  bearing  plate  screw.  Change 
calculated  dimensions  to  nearest  ^  or  |  inch,  according  to  judgment.  Let 
a  =  7  inches  and  b  =  8|  inches.  Scale  6  in.  =  1  ft. 


BALL  BEARING 

Ball  bearings  are  used  in  many  machines  to  reduce  frictional 
resistance  between  bearings  and  journals,  or  shafts. 

The  drawing  shows  three  views  and  details  of  a  ball  bearing 
suitable  for  a  horizontal  one-inch  shaft.  The  races  are  of  hard- 
ened steel  and  the  casing  is  of  cast  iron.  The  inner  race  is 
securely  fastened  by  means  of  a  nut  threaded  on  the  end  of  the 
shaft,  while  the  outer  races  are  secured,  after  being  properly 
adjusted,  by  tightening  the  casing  with  a  stud  and  nut  as  shown. 

Problem  1. — Make  an  assembly  drawing  having  three  views  and  details 
of  a  bearing  as  shown.  Let  o  =  2f  inches. 

Problem  2. — Draw  front  and  top  views  of  a  bearing  with  the  dimensions 
shown.  Show  top  view  in  full-section  at  the  axis  of  the  shaft.  Draw  two 
views  of  the  inner  race  and  two  views  of  one  outer  race  showing  each  in 
half-section.  Let  a  =  3  inches. 

Problem  3. — Make  a  detail  drawing  of  the  bearing  shown.  Show  three 
views  of  the  casing,  two  views  of  the  inner  race,  two  views  of  one  outer 
race,  and  one  view  of  the  stud  and  nut.  Let  a  =  2f  inches. 


MACHINE  DETAILS 


141 
PLATE  111 


SQUARE  THREAD 

SCREW  JACK 


BALL  BEARING 


PLATE  112 


PART  III 
TABLES 

LIST  OF  TABLES 

I.  Cap  Screws. 
II.  U.  S.  Standard  Bolts  and  Nuts 

III.  Machine  Screws. 

IV.  Briggs  Standard  Pipe  Threads. 
V.  Set  Screws. 

VI.  Gib  Keys. 

VII.  Feather  Keys  or  Splines. 
VIII.  Automobile  Screws  and  Nuts. 
IX.  Jarno  Tapers. 
X.  Morse  Tapers. 
XI.  Decimal  Equivalents. 
XII.  Areas  and  Circumferences  of  Circles. 
Conventional  Section  Lines. 


143 


144 


MECHANICAL  DRAWING  PROBLEMS 


HS 

« 

* 

Hi 

* 

-5 

^ 

HS 

•ft 

- 

§ 

§ 

S 

g 

§ 

a 

s 

2 

g 

cc 

* 

Hi 

H! 

* 

~ 

* 

* 

* 

„ 

s 

•B 

« 

Hi 

~ 

Hi 

* 

HS 

* 

» 

HS 

HS 

is 

* 

* 

•e 

HS 

^t 

• 

HS 

H: 

HS 

« 

Hi 

•B 

., 

Hi 

* 

H! 

HS 

o 

3 

1 

g 

g 

s 

s 

DO 

fg 

3 

« 

HI 

o 

* 

-B 

Hi 

« 

a 

* 

* 

HS 

* 

HS 

«, 

- 

- 

- 

j. 

H! 

- 

rt 

- 

- 

-B 

-* 

HS 

* 

•B 

* 

* 

< 

* 

HS 

* 

HS 

HS 

Hi 

* 

H; 

H. 

Hi 

•B 

HS 

1 

o 

1 

I 

et 

s 

I 

1 

3 

S 

§ 

a 

* 

* 

- 

* 

HS 

* 

- 

* 

* 

ri 

* 

* 

HS 

« 

HS 

* 

55 

as 

- 

* 

* 

HS 

- 

* 

* 

H. 

^ 

s: 

* 

HS 

HB 

* 

HH 

as 

-' 

* 

- 

HS 

* 

* 

* 

HS 

„ 

* 

HS 

* 

4s 

* 

- 

* 

« 

H 

«. 

g 

c 

c 

* 

* 

< 

HS 

« 

H. 

HS 

« 

» 

* 

« 

ss 

« 

* 

- 

,, 

g 

OB 

B 

^ 

eo 

N 

— 

o 

^ 

H! 

_„ 

HS 

„. 

HS 

_., 

HS 

.., 

w. 

TABLES 


145 


TABLE  II.— U.  S.  STANDARD  BOLTS  AND  NUTS 

'o 


^K  r 

L 


D  =  Diameter 

No.  of  threads 
per  inch 

ii 

i! 

A  =  li  D  +  l 
B  =  1|  D  +  J 

-J 

E  =  D 

Rough 

Finished 

A 

B          c     |E 

A 

B      |       C      |       E 

J 

20 

.026 

1 

H 

i 

i 

A 

i 

A 

A 

A 

18 

.045 
.068 

If 

« 

if 

A 

H 

M 

i 

i 

1 

16 

H 

li 

H 

1 

-I 

M 

A 

A 

A 

14 

.093 

H 

H 

If 

A 

H 

M 

1 

1 

1 

13 

.126 

1 

1A 

A 

i 

H 

H 

A 

A 

A 

12 
11 
10 

9 
8 

7 

.162 
.202 
.302 

li 

H 

H 

A 

H 

1* 

i 

i 

! 

1* 

1H 

H 

1 

l 

i* 

A 

A 

I 

"T~ 
i 
H 

U 

m 

I 

i 

1A 

1« 

H 

tt 
~S 

.419 

IA 

i« 

If 

1 

H 

m 

H 

.551 

U 

H          H 

i 

1A 

i« 

if 

if 

.693 

1« 

2A    !    M 

li 

U 

2^ 

1A 

1A 

a 

7 

.889 

2           2^        1 

U 

1H 

2H     |  1A 

'1A 

10 


146 


MECHANICAL  DRAWING  PROBLEMS 
TABLE  in.— MACHINE  SCREWS 


Round  Flat  Fillister 

A.S.M.E.  STANDARD 


No. 

No.  of 
Threads 

D 

A 

B 

C 

E 

F 

G 

H 

0 

80 

.060 

.112 

.029 

.106 

.042 

.0894 

.0496 

.0376 

1 

72 

.073 

.138 

.037 

.130 

.051 

.1107 

.0609 

.0461 

2 

64 

.086 

.164 

.045 

-.154 

.060 

.132 

.0725 

.0548 

3 

56 

.099 

.190 

.052 

.178 

.069 

.153 

.0838 

.0633 

4 

48 

.112 

.216 

.060 

.202 

.078 

.1747 

.0953 

.0719 

5 

44 

.125 

.242 

.067 

.226 

.087 

.196 

.1068 

.0805 

6 

40 

.138 

.262 

.075 

.250 

.096 

.217 

.1180 

.089 

7 

36 

.151 

.294 

.082 

.274 

.105 

.2386 

.1296 

.0976 

8 

36 

.164 

.320 

.090 

.298 

.114 

.2599 

.1410 

.1062 

9 

32 

.177 

.346 

.097 

.322 

.123 

.2813 

.1524 

.1148 

10 

30 

.190 

.372 

.105 

.346 

.133 

.3026 

.1639 

.1234 

12 

28 

.216 

.424 

.120 

.394 

.151 

.3452 

.1868 

.1405 

14 

24 

.242 

.472 

.135 

.443 

.169 

.3879 

.2097 

.1577 

16 

22 

.268 

.528 

.150 

.491 

.187 

.4305 

.2325 

.1748 

18 

20 

.294 

.580 

.164 

.539 

.205 

.4731 

.2554 

.192 

20 

20 

.320 

.632 

.179 

.587 

.224 

.5158 

.2783 

.2092 

22 

18 

.346 

.682 

.194 

.635 

.242 

.5584 

.3011 

.2263 

24 

16 

.372 

.732 

.209 

.683 

.260 

.601 

.3240 

.2435 

26 

16 

.398 

.788 

.224 

.731 

.278 

.6437 

.3469 

.2606 

28 

14 

.424 

.840 

.239 

.779 

.296 

.6863 

.3698 

.2778 

30 

14 

.450 

.892 

.254 

.827 

.315 

.727 

.4024 

.295 

TABLES  147 

TABLE  IV.— BRIGGS  STANDARD  PIPE  THREADS 


s  Length  of  perfect  threads 


Nominal 
inside 
diam. 

Actual 
inside 
diam. 

Actual 
outside 
diam. 

No.  of 
threads 
per  inch 

Internal 
area 

Length, 
perfect 
threads 

Diam. 
drill 

1 

.270 

.405 

27 

.057 

A 

Ii 

i 

.364 

.540 

18 

.104 

A 

H 

f 

.494 

.675 

18 

.191 

if 

if 

i 

.623 

.840 

14 

.304 

! 

H 

'i 

.824 

1.050 

14 

.533 

H 

H 

i 

1.048 

1.315 

ill 

.861 

1 

1A 

ji 

1.380 

1.660 

HI 

1.496 

If 

1*1 

ii 

1.610 

1.900 

m 

2.036 

A 

if* 

2 

2.067 

2.375 

m 

3.356 

H 

2A 

2| 

2.468 

2.875 

8 

4.780 

H 

2H 

3 

3.067 

3.500 

8 

7.383 

Ii 

3A 

3i 

3.548 

4.000 

8 

9.887 

i 

3H 

4 

4.026 

4.500 

8 

12.730 

1A 

4^ 

41 

4.508 

5.000 

8 

15.961 

i* 

4H 

5 

5.045 

5.563 

8 

19.986 

1A 

6| 

148 


MECHANICAL  DRAWING  PROBLEMS 
TABLE  V.— SET  SCREWS 


Round  Cup  Hanger       Headless 

Point  Point  Point 


TABLE  VI.— GIB  KEYS 


Taper  i  inch  per  foot 


A 

B 

C1 

D 

IA 

B 

° 

D 

A 

B 

c 

D 

i 

1 

1 

A 

A 

A 

! 

H 

t 

3 

H 

1 

A 

A 

A 

& 

i 

i 

1 

H 

H 

H 

1A 

if 

i 

1 

t* 

H 

A 

A 

i 

ft 

1 

1 

H 

1 

A 

A 

A 

H 

1 

1 

1* 

If 

H 

» 

U 

IA 

f 

I 

H 

if 

H 

H 

l& 

If 

1 

1 

H 

ti 

TABLE  VII.— FEATHER  KEYS  OR  SPLINES 


n 


Diameter  of  shaft  1  1  i  1  i 

H     if 

2 

21 

3 

3* 

4 

\ 

6 

Width  of  feather  \      & 

I    !  A 

» 

1 

,f 

i 

i 

li 

61 

Thickness  of  -feather   .  |  f  |   A 

\    .  A 

f 



f 

i 

1 

1J 

If 

U 

TABLES  149 

TABLE  VIU.— AUTOMOBILE  SCREWS  AND  NUTS 


S.  A.  E.  Standard 
n  =  no.  of  threads  per  inch;     d  =  diam.  cotter  pin 


D 

A 

B 

c 

E 

F 

G 

H 

I 

J 

n 

d 

i 

ft 

A 

ft 

A 

A 

A 

A 

A 

I 

28 

A 

A 

1 

it 

H 

A 

& 

ft 

A 

A 

U 

24 

A 

! 

A 

& 

H 

ft 

1 

U 

i 

i 

& 

24 

A 

A 

I 

ft 

I 

A 

i 

H 

i 

1 

H 

20 

A 

} 

I 

1 

A 

A 

1 

A 

A 

1 

1 

20 

A 

ft 

1 

H 

H 

& 

i 

H 

A 

A 

H 

18 

i 

I 

tt 

H 

H 

A 

1 

ft 

i 

A 

H 

18 

i 

H 

i 

a 

it 

A 

i 

H 

i 

ft 

1A 

16 

i 

i 

1A 

& 

H 

& 

i 

H 

i 

A 

U 

16 

1 

1 

H 

i* 

tt 

A 

i 

& 

i 

A 

ift 

14 

i 

i 

1A 

i 

1 

A 

i 

i 

i 

ft 

li 

14 

i 

150 


MECHANICAL  DRAWING  PROBLEMS 


TABLE  IX.— JARNO  TAPERS 


No. 

A 

B 

C 

No. 

A 

B 

C 

No. 

A 

B 

C 

2 

.250 

.20 

1 

9 

1.125 

.90 

4* 

16 

2.000 

1.60 

8 
8* 

9 
~9T~ 

3 

.375 

.30 

H 

2 

10 

1.250 

1.00 

5 
51 

17 
18 

2.125 
2.250 

1.70 
1.80 

4 

.500 

.40 

11 

1.375 

1.10 

5 

.625 

.50 

2* 

12 

1.500 

1.20 

6 

19 

2.375 

1.90 

6 

7 
8 

.750 

.60 

3 

13 

14 

1.625 

1.30 

6* 

20 

2.500 

2.00 

10 

.875 

.70 

Si 

1.750 

1.40 

7 



1.000 

.80 

4 

15 

1.875 

1.50 

n 

TABLE  X.— MORSE  TAPERS 


No. 

A 

B    j    C 

No. 

A 

B 

C 

No. 

A 

B 

C 

0 

.356  .252 

2 

3 
4 

.938 

.778 

3& 

6 

2.494 

2.116 

7i 

1 

.475  .369 

1 

2* 

1.231 

1.748 

1.020 
1.475 

4& 

7 

3.270 

2.750 

10 

2 

,00 

.572 

2& 

5 

5A 

TABLES 


151 


TABLE  XI.— DECIMALS  OF  AN  INCH  FOR  EACH 


Ads. 

Aths. 

Decimal. 

Fraction.    -fads. 

*ths. 

Decimal. 

Fraction. 

1 

.015625 

33 

.515625 

1 

2 

.03125 

17 

34 

.53125 

3 

.046875 

35 

.546875 

2 

4 

.0625 

1-16      18 

36 

.5625 

9-16 

5 

.078125 

37 

.578125 

3 

6 

.09375 

19 

38 

.59375 

7 

.  109375 

39 

.609375 

4 

8 

.125 

1-8      20 

40 

.625 

5-8 

9 

.140625  1                  41 

.  640625 

5 

10 

.  15625             21 

42 

.65625 

11 

.171875 

43 

.671875 

6 

12 

.1875     3-16      22 

44 

.6875 

11-16 

13 

.203125 

45 

.703125 

7 

14 

.21875            23 

46 

.71875 

15 

.234375 

47 

.734375 

8 

16 

.25      1-4      24      48 

.75 

3-4 

17 

.  265625                  49 

.  765625 

9 

18 

.28125            25 

50 

.78125 

19 

.296875                  51 

.  796875 

10 

20 

.3125 

5-16      23      52 

.8125 

13-16 

21 

.328125 

53 

.828125 

11 

22 

.34375            27 

54 

.84375 

23 

.  359375                  55 

.859375 

12 

24 

.375    :  3-8       28      56 

.875 

7-8 

25 

.390625                  57    .890625 

13 

26 

.40625 

29      58 

.90625 

27 

.421875 

59 

.921875 

14 

28 

.4375 

7-16     30      60 

.9375 

15-16 

29 

.453125  j                 61 

.953125 

15    30 

.46875  '          31 

62 

.96875 

31 

.484375 

63 

.984375 

16    32 

.5       1-2      32      64   1.         J 

152 


MECHANICAL  DRAWING  PROBLEMS 


TABLE  XII.— AREAS  AND  CIRCUMFERENCES  OF  CIRCLES  FROM 
1  TO  10 


Dia.  j   Area 

Circum.  ||  Dia.  j   Area 

Circum.   Dia. 

Area 

Circum. 

1 

0.00077 
0.00173 
0.00307 
0.00690 
0.01227 
0.01917 
0.02761 
0.03758 

0.098175 
0.147262 
0.196350 
0.294524 
0.392699 
0.490874 
0.589049 
0.687223 

2 

A 

1 

3.1416 
3.3410 
3.5466 
3.7583 
3.9761 
4.2000 
4.4301 
4.6664 

6.28319 
6.47953 
6.67588 
6.87223 
7.06858 
7.26493 
7.46128 
7.65763 

5 

16 
1$ 
T6 

19.635 
20.129 
20.629 
21.135 
21.648 
22  .  166 
22.691 
23.221 

15.7080 
15.9043 
16.1007 
16.2970 
16.4934 
16.6897 
16.8861 
17.0824 

1 

1 

0  .  04909 
0.06213 
0.07670 
0.09281 
0.11045 
0.12962 
0.15033 
0.17257 

0.785398 
0.883573 
0.981748 
1.07992 
1.17810 
1  .  27627 
1  .  37445 
1.47262 

i 

tt 

4.9087 
5.1572 
5.4119 
5.6727 
5.9396 
6.2126 
6.4918 
6.7771 

7.85398 
8.05033 
8.24668 
8.44303 
8.63938 
8.83573 
9  .  03208 
9.22843 

\ 

i 

fr 
1 

-I 
i 

23.758 
24.301 
24.850 
25.406 
25.967 
26.535 
27  .  109 
27.688 

17.2788 
17.4751 
17.6715 
17.8678 
18.0642 
18.2605 
18.4569 
18.6532 

i 

0.19635 
0.22166 
0.24850 
0.27688 
0.30680 
0.33824 
0.37122 
0.40574 

1  .  57080 
1.66897 
1.76715 
1  .  86532 
1.96350 
2.06167 
2.15984 
2.25802 

3 

I 

A 

7.0686 
7.3662 
7.6699 
7.9798 
8.2958 
8.6179 
8.9462 
9.2806 

9.42478 
9.62113 
9.81748 
10.0138 
10.2102 
10.4065 
10.6029 
10.7992 

6 

28.274 
29.465 
30.680 
31.919 
33.183 
34.472 
35.785 
37.122 

18.8496 
19.2423 
19.6350 
20.0277 
20.4204 
20.8131 
21.2058 
21.5984 

1 

8 

0.44179 
0.47937 
0.51849 
0.55914 
0.60132 
0.64504 
0.69029 
0.73708 

2.35619 
2.45437 
2.55254 
2.65072 
2.74889 
2.84707 
2.94524 
3.04342 

1 

H 

9.6211 
9.9678 
10.321 
10.680 
11.045 
11.416 
11.793 
12.177 

10.9956 
11.1919 
11.3883 
11.5846 
11.7810 
11.9773 
12.1737 
12.3700 

7 

i 

if 

38.485 
39.871 
41.282 
42.718 
44.179 
45  .  664 
47.173 
48.707 

21.9911 
22.3838 
22.7765 
23.1692 
23.5619 
23  .  9546 
24  .  3473 
24.7400 

3 

0.78540 
0.88664 
0.99402 
1  .  1075 
1.2272 
1.3530 
1.4849 
1.6230 

3.14159 
3.33794 
3.53429 
3.73064 
3.92699 
4.12334 
4.31969 
4.51604 

16 
1$ 

£ 

12.566 
12  .  962 
13.364 
13.772 
14.186 
14.607 
15.033 
15.466 

12.5664 
12.7627 
12.9591 
13.1554 
13.3518 
13.5481 
13.7445 
13.9408 

8 

. 

i 

50.265 
51.849 
53.456 
55.088 
56.745 
58  .  426 
60.132 
61.862 

25.1327 
25.5224 
25.9181 
26.3108 
26.7035 
27.0962 
27.4889 
27.8816 

I 

I 
H 

1.7671 
1.9175 
2  .  0739 
2.2365 
2.4053 
2.5802 
2.7612 
2.9483 

4.71239 
4.90874 
5.10509 
5.30144 
5.49779 
5.69414 
5.89049 
6.08684 

1 

f 
H 

15.904 
16.349 
16.800 
17.257 
17.721 
18.190 
18.665 
19.147 

14.1372 
14.3335 
14.5299 
14.7262 
14.9226 
15.1189 
15.3153 
15.5116 

9 

63.617 
65.397 
67.201 
69.029 
70.882 
72.760 
74.662 
76.589 

28.2743 
28.6670 
29.0597 
29.4524 
29.8451 
30.2378 
30.6305 
31.0232 

10 

78.540 

31.4159 

TABLES 


153 


CONVENTIONAL  SECTION  LINES 


CAST  IRON 


WROUGHT  IRON 


MALLEABLE  IRON 


CAST  .STEEL 


COPPER 


BRASS  OR  BRONZE 


BABBITT 


VULCANITE 


GLASS 


WATER 


A     000037032     o 


